{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian data analysis - PyStan demos\n",
    "Author: Aki Vehtari, Tuomas Sivula, Co-authors: Lassi Meronen, Pellervo Ruponen\n",
    "\n",
    "Last modified 2018-Dec.\n",
    "\n",
    "License: CC-BY\n",
    "\n",
    "This notebook contains several examples of how to use [Stan](http://mc-stan.org) in python with [PyStan](http://pystan.readthedocs.org). This notebook assumes basic knowledge of Bayesian inference and MCMC. The Stan models are stored in separate .stan-files. The examples are related to Bayesian data analysis course by Aki Vehtari."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting up the PyStan environment\n",
    "\n",
    "We begin by importing the PyStan module as well at the matplotlib module for basic graphics facilities.\n",
    "\n",
    "We also import some utilities by Michael Betancourt and introduced in [PyStan workflow case study](http://mc-stan.org/users/documentation/case-studies/pystan_workflow.html) in module `stan_utility`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import pystan\n",
    "import arviz as az # For visualization and loo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "# add utilities directory to path\n",
    "import os, sys\n",
    "util_path = os.path.abspath(os.path.join(os.path.pardir, 'utilities_and_data'))\n",
    "if util_path not in sys.path and os.path.exists(util_path):\n",
    "    sys.path.insert(0, util_path)\n",
    "\n",
    "# import from utilities\n",
    "import stan_utility"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [],
   "source": [
    "# edit default plot settings\n",
    "plt.rc('font', size=12)\n",
    "az.style.use('seaborn-darkgrid')\n",
    "mpl.rcParams['figure.figsize'] = [7.0, 5.4]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bernoulli model\n",
    "\n",
    "Toy data with sequence of failures (0) and successes (1). We would like to learn about the unknown probability of success. In following, we denote this probability with theta."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = dict(N=10, y=[0,1,0,0,1,1,1,0,1,0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bernoulli model with a Beta(1,1) (uniform) prior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "// Bernoulli model\n",
      "data {\n",
      "  int<lower=0> N;\n",
      "  int<lower=0,upper=1> y[N];\n",
      "}\n",
      "parameters {\n",
      "  real<lower=0,upper=1> theta;\n",
      "}\n",
      "model {\n",
      "  theta ~ beta(1,1);\n",
      "  y ~ bernoulli(theta);\n",
      "}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with open('bern.stan') as file:\n",
    "    print(file.read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given the Stan program we then use the `compile_model` method of `stan_utility` module to compile the Stan program into a C++ executable. This utility function automatically saves a cached version of the compiled model to the disk for possible future use."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    }
   ],
   "source": [
    "model = stan_utility.compile_model('bern.stan')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Getting the model again with the utility function uses the cached version automatically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    }
   ],
   "source": [
    "del model\n",
    "model = stan_utility.compile_model('bern.stan')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sample from the posterior, show the summary and plot the histogram of the posterior draws. In addition, plot estimated posterior density with arviz posterior plot and 95% credible interval. We recommend explicitly specifying the seed of Stan's random number generator, as we have done here, so that we can reproduce these exactly results in the future, at least when using the same machine, operating system, and interface. This is especially helpful for the more subtle pathologies that may not always be found, which results in seemingly stochastic behavior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inference for Stan model: anon_model_4586f2dc76604848221fafe6413762a9.\n",
      "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
      "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
      "\n",
      "        mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
      "theta    0.5  3.7e-3   0.14   0.24    0.4    0.5    0.6   0.76   1420    1.0\n",
      "lp__   -8.84    0.02   0.71 -10.87  -9.04  -8.57  -8.37  -8.32   1690    1.0\n",
      "\n",
      "Samples were drawn using NUTS at Wed Dec 19 11:19:21 2018.\n",
      "For each parameter, n_eff is a crude measure of effective sample size,\n",
      "and Rhat is the potential scale reduction factor on split chains (at \n",
      "convergence, Rhat=1).\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 504x388.8 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 460.8x345.6 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit = model.sampling(data=data, seed=194838)\n",
    "print(fit)\n",
    "samples = fit.extract(permuted=True)\n",
    "\n",
    "plt.hist(samples['theta'], 33, color='lightblue', edgecolor='grey')\n",
    "plt.xlabel(r'Probability of success (theta)')\n",
    "plt.ylabel('Amount of draws')\n",
    "\n",
    "# Plot with arviz plot_posterior.\n",
    "#    - round_to: sets accuracy of values in plot\n",
    "az.plot_posterior(fit, var_names=['theta'], credible_interval=0.95, round_to=2)\n",
    "plt.xlabel(r'Probability of success (theta)')\n",
    "plt.ylabel('Relative density');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binomial model\n",
    "\n",
    "Instead of sequence of 0's and 1's, we can summarize the data with the number of experiments and the number successes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = dict(N=10, y=7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then we use Binomial model with Beta(1,1) prior for the probability of success."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "// Binomial model with beta(1,1,) prior\n",
      "data {\n",
      "  int<lower=0> N;\n",
      "  int<lower=0> y;\n",
      "}\n",
      "parameters {\n",
      "  real<lower=0,upper=1> theta;\n",
      "}\n",
      "model {\n",
      "  theta ~ beta(1,1);\n",
      "  y ~ binomial(N,theta);\n",
      "}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with open('binom.stan') as file:\n",
    "    print(file.read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sample from the posterior and plot the posterior. The histogram should look similar as in the Bernoulli case, except that now the number of successes is 7 instead of 5."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x388.8 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 460.8x345.6 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = stan_utility.compile_model('binom.stan')\n",
    "fit = model.sampling(data=data, seed=194838)\n",
    "samples = fit.extract(permuted=True)\n",
    "plt.hist(samples['theta'], 33, color='lightblue', edgecolor='grey')\n",
    "plt.xlabel(r'Probability of success (theta)')\n",
    "plt.ylabel('Amount of draws')\n",
    "\n",
    "az.plot_posterior(fit, var_names=['theta'], credible_interval=0.95, round_to=2)\n",
    "plt.xlabel(r'Probability of success (theta)')\n",
    "plt.ylabel('Relative density');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we re-run the model with a new data (now number of successes being 70 out of 100). The previously compiled Stan program is re-used making the re-use faster."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UCY0bNwYA9OzZEydPnkRJSQkcHR0NXiAREZGpPPEzSZlMhsGDB8PK6r9N5XI5A5KIiCyepBt3Wrdujd9//93QtRAREZkVSZ9JBgQEYPz48QgNDUWjRo0gk8n061577TWDFUdERGRKkkLy9OnTaNq0KU6ePFlhuUwmY0gSEZHF4titREREIkRDsry8XNIG/npDDxERkSURDck2bdpU+OxRDCddJiIiSyUakgcOHNB/ffjwYezbtw8TJ05EkyZNcOvWLaxZswb9+vUzSpFERESmIBqSTZs21X+9bt06bNu2Dc899xwAoGXLlmjXrh1effVVvP7664avkoiIyAQkfaBYWFiIP//8s8KyoqIiFBZKG4eyuLgY77//PoKDg6FSqTBkyBAcOXJEv/7EiRMYMGAAfHx8EB4ejps3b1Z47XvvvQdfX18EBQUhKSlJ0j6JiIielaSQDA0NxejRo7FlyxYcOXIEW7ZswdixYxEaGippJ6WlpWjcuDE2btyIn376CdOnT8f06dORnZ2NvLw8REZGYtq0aTh58iTatWuHGTNm6F8bHx+Pa9eu4dChQ9iwYQMSExPx/fffP11viYiIqkHSIyCzZ89G8+bNsXv3bty9exeurq544403MHz4cEk7cXBwQFRUlP774OBgNGvWDBcuXEB+fj48PT0xcOBAAEBUVBS6dOmCrKwsuLu7IyUlBYsXL4aTkxOcnJwQFhaGlJQU9OjR4ym6S0REJJ2kkLSyssLIkSMxcuTIGtlpbm4url69Cg8PD2zevBleXl76dQ4ODmjevDmuXLmCBg0a4N69e/D29tav9/b2rnBTERERkaFICsmaVFJSgujoaISGhsLd3R1arRYuLi4V2igUCmg0Gmi1WgCAUqnUr1MqldBoNJW2q1DYwcbG2rDFG5m1tRWcnR1MXYbBsH9kClKOiaUfO/ZPOqOGZHl5Od5++23Y2tpi7ty5AB6eOarV6grtNBoNHB0d4eDwsJNqtRp2dnb6r6uagUSt1hm4euNzdnZAfr7W1GUYjCX0jxMp1z5SfuYs4WfzcepS/1xdlU9o/XhGC0lBEDBnzhzk5uZizZo1sLW1BQB4enoiJSVF306r1eL69evw8PCAk5MTXF1dkZmZiaCgIABAZmYmPDw8jFU20WNJnUgZ4GTK5kBmZY2VK+Oe2E7x3HOIGDXOCBWRuRMNyeHDh+Orr74CAPz73/9GZGTkM+0oJiYGWVlZSEpKgr29vX5537598cknn2Dfvn3o1asXVqxYAS8vL7i7uwMAhg4dioSEBLRr1w65ublITk7GokWLnqkWIqqbhPIySX/U8A8aekT0EZCrV69Cp3t4CfOzzz57pp3cvHkTW7ZsQUZGBrp16waVSgWVSoWdO3fCxcUF8fHxWLp0KTp16oRz584hLu6/f+lNnToVL7zwAoKDgxEeHo6xY8fyzlYiIjIK0TPJPn36oH///mjatCl0Oh3eeOONKtt9/vnnT9xJ06ZNcfHiRdH1gYGB2Lt3b5Xr5HI5YmNjERsb+8T9EBER1STRkIyNjUV6ejpu3ryJ8+fPc95IIiKqcx57446/vz/8/f1RUlIieXQdIiIiSyHp7tbXXnsNaWlp2L59O+7evQs3NzcMGTIEXbp0MXR9REREJiNp7Nbk5GRMnz4drq6u6Nu3L9zc3DBr1iz93a9ERESWSNKZZGJiIpKSkioMDzdw4EBMnTpV8vitREREtY2kM8n8/Hz9c4uPvPjiiygoKDBIUUREROZAUkj6+vpi8eLF+jkltVotPvnkE6hUKoMWR0REZEqSLrfOnz8fM2bMgL+/P5ycnFBQUACVSoUlS5YYuj4iIiKTkRSSbm5u+Pzzz3Hnzh393a2NGjUydG1EREQmVa0Bzhs1asRwJCKiOkPSZ5JERER1EUOSiIhIBEOSiIhIhKSQDAgIqHJ5165da7QYIiIicyIpJEtKSqpcVl5eXuMFERERmYvH3t36+uuvQyaTobi4uNJ8knfu3OFgAkREZNEeG5JhYWEQBKHSfJIymQzPP/88ZwEhIiKL9tiQfDSHpI+PT6WxW4mILJXMyhorV8ZJauuoUOLNiPEGrohMRdJgAu7u7jh27BgyMjKg1WorrJs2bZpBCiMiMhWhvAztR0yQ1Pb8l6sNXA2ZkqSQXLBgAfbs2YPOnTujXr16hq6JiIjILEgKyW+++QY7duxA48aNDV0PERGR2ZD0CEj9+vWhVCoNXQsREZFZkXQmOXr0aERHR2PixIlo0KBBhXUvvPCCQQojIiIyNUkhOW/ePADA4cOHKyyXyWTIyMio6ZqIiIjMgqSQzMzMNHQdREREZocDnBMREYmQdCb5aHi6qnz++ec1WhAREZG5kBSSYWFhFb6/d+8etm3bhsGDBxukKCIiInMgKSQfDU/3V/3798d7772HyMjIGi+KiIjIHDz1Z5INGzbExYsXa7IWIiIisyLpTHLr1q0Vvi8qKsK3336Ljh07St7Rpk2b8PXXX+PSpUsICQnB4sWLAQDZ2dno06cPHBwc9G3HjRuHKVOmAACKi4sRExODffv2oV69ehg3bhxGjx4teb9ERERPS1JI7tixo8L3Dg4OUKlU+J//+R/JO3Jzc8PkyZNx9OhR6HS6SutPnToFG5vK5cTHx+PatWs4dOgQcnNzERERAXd3d/To0UPyvomIiJ6GpJDcuHHjM++oX79+AIDz588jJydH8utSUlKwePFiODk5wcnJCWFhYUhJSWFIEhGRwUkKSQC4evUqvvnmG9y9exdubm4ICQlBixYtaqyQ4OBgyGQyBAUFYfbs2XBxcUFBQQHu3bsHb29vfTtvb28cOHCgxvZLREQkRlJIHjx4ENHR0QgODkaTJk3w+++/49VXX8Unn3yCPn36PFMB9evXx9atW9G6dWvk5+djwYIFmD17NtauXaufu/Kvg6srlUpoNJpK21Eo7GBjY/1MtZgba2srODs7PLlhLWXp/aO6o7b9HFv6715N9k9SSC5duhQrV65Ely5d9MvS0tLw0UcfPXNIOjo6on379gCABg0aYO7cuejWrRvUarX+Zh61Wg07Ozv9146OjpW2o1ZX/pyztnN2dkB+vvbJDWspS+8f1R217efY0n/3/to/V9dnm8FK0iMgd+7cgb+/f4Vlfn5+uHPnzjPtvCqPRvYRBAFOTk5wdXWtMHZsZmYmPDw8any/REREfycpJL29vfHZZ59VWJaUlITWrVtL3lFpaSl0Oh3Ky8tRVlYGnU6H0tJSnD17Fr/99hvKy8vx4MEDLFy4EAEBAfpLrEOHDkVCQgIKCgqQlZWF5OTkKgc3ICIiqmmSp8p66623sGHDBjRu3Bi3b99GvXr1sGrVKsk7SkhIwL///W/99zt37kRkZCRatmyJuLg45OXlQaFQIDAwEHFxcfp2U6dORUxMDIKDg2Fvb4/x48fzzlYiIjIKSSHp7u6O3bt34+eff9bf3erj4wNbW1vJO4qKikJUVFSV60JCQkRfJ5fLERsbi9jYWMn7IiIiqgmSHwGxsbGp9LkkERGRJZM86fKiRYuQmZmpfyxDEATIZDL88ssvBi2QiIjIVCSF5MyZM9GvXz988MEHsLe3N3RNREREZkFSSObm5mLatGmiEy8TWZL1G9ZAoy40dRlEZAYkheTQoUORmpqKV155xdD1EJmcRl2I9iMmSGp7/svVBq6GiExJUkhOmDAB//znP/Gf//wHzz//fIV1GzZsMEhhREREpiYpJKdOnYpmzZqhb9+++uHhiIiILJ2kkMzIyEBaWhrkcrmh6yEiIjIbkoal8/f3R1ZWlqFrISIiMiuSziSbNWuGMWPGoG/fvpU+k5w2bZpBCiMiIjI1SSFZVFSEXr16oaSkxCAzfxAREZkjSSEpNm5qeXl5jRZDRERkTiR9Jvl3Fy9exP/+7/9yNg4iIrJokgc4z8vLQ2pqKrZv347MzEz4+flhzpw5hqyNiIjIpB4bkiUlJTh48CBSUlJw7NgxNG/eHC+//DJu3bqFTz/9tNJNPERERJbksSEZFBQEmUyGYcOGISoqCm3btgUAbN682SjFERERmdJjP5P08vJCYWEhzp49i/Pnz6OgoMBYdREREZncY88kN27ciJs3b2L79u347LPPsHDhQnTr1g1arRalpaXGqpGIyGzJrKyxcmWcpLaOCiXejBhv4IqoJj3xxp2mTZtiypQpmDJlCtLT07Fjxw5YWVnhlVdewauvvoq3337bGHUSEZklobyMs8ZYMMl3twIPh6fz9/fHBx98gP3792P79u2GqouIiMjkqhWSj9jZ2SEkJAQhISE1XQ8REZHZeKrBBIiIiOoChiQREZEIhiQREZEIhiQREZEIhiQREZEIhiQREZEIhiQREZEIhiQREZEIhiQREZGIpxpx52ls2rQJX3/9NS5duoSQkBAsXrxYv+7EiROYP38+bt++jQ4dOmDx4sVo2rQpAKC4uBgxMTHYt28f6tWrh3HjxmH06NHGKpssxPoNa6BRF5q6DCKqZYwWkm5ubpg8eTKOHj0KnU6nX56Xl4fIyEgsXLgQvXv3xrJlyzBjxgx89dVXAID4+Hhcu3YNhw4dQm5uLiIiIuDu7o4ePXoYq3SyABp1IQehJqJqM9rl1n79+uGll16Cs7NzheX79++Hp6cnBg4cCDs7O0RFRSEzMxNZWVkAgJSUFEyePBlOTk5wd3dHWFgYUlJSjFU2ERHVYSb/TPLy5cvw8vLSf+/g4IDmzZvjypUrKCgowL179+Dt7a1f7+3tjStXrpiiVCIiqmOMdrlVjFarhYuLS4VlCoUCGo0GWq0WAKBUKvXrlEolNBpNpe0oFHawsbE2bLFGZm1tBWdnB1OXYTCW3j+iqpjDz7yl/+7VZP9MHpIODg5Qq9UVlmk0Gjg6OsLB4WEn1Wo17Ozs9F87OjpW2o5arau0rLZzdnZAfr7W1GUYjKX3j6gq5vAzb+m/e3/tn6ur8gmtH8/kl1s9PT2RmZmp/16r1eL69evw8PCAk5MTXF1dK6zPzMyEh4eHKUolIqI6xmghWVpaCp1Oh/LycpSVlUGn06G0tBR9+/bF5cuXsW/fPuh0OqxYsQJeXl5wd3cHAAwdOhQJCQkoKChAVlYWkpOTERoaaqyyiYioDjNaSCYkJKBDhw5YvXo1du7ciQ4dOiAhIQEuLi6Ij4/H0qVL0alTJ5w7dw5xcXH6102dOhUvvPACgoODER4ejrFjx/LxDyIiMgqjfSYZFRWFqKioKtcFBgZi7969Va6Ty+WIjY1FbGysIcsjIiKqxOSfSRIREZkrhiQREZEIhiQREZEIhiQREZEIkw8mQERUV8isrLFyZdyTGwJwVCjxZsR4A1dET8KQJCIyEqG8jLPR1DK83EpERCSCIUlERCSCIUlERCSCIUlERCSCIUlERCSCIUlERCSCIUlERCSCz0lSrbZ+wxpo1IWmLoOILBRDkmo1jbpQ0sPZfDCbiJ4GL7cSERGJYEgSERGJYEgSERGJ4GeSZHZ4Mw4RmQuGJJkdqTfjALwhh4gMi5dbiYiIRDAkiYiIRDAkiYiIRDAkiYiIRDAkiYiIRDAkiYiIRDAkiYiIRDAkiYiIRDAkiYiIRDAkiYiIRDAkiYiIRJhNSIaHh6N9+/ZQqVRQqVTo37+/fl1qaiqCg4PRsWNHTJ48Gfn5+SaslIiI6gqzGuD8ww8/RFhYWIVlly9fxocffojVq1ejTZs2+PDDDzF//nwsXbrURFUSERmezMoaK1fGPbGdo0KJNyPGG6GiusmsQrIqqamp6N27Nzp16gQAmDZtGgYNGgS1Wg2FQmHi6oiIDEMoL5M0Gw5nwjEsswrJJUuW4P/+7//QsmVLzJgxA507d8bly5ehUqn0bZo3bw5bW1tcvXoV7dq10y9XKOxgY2NtirINxtraCs7ODqYuw2AsvX9ExlLd3yNL/92ryf6ZTUhGR0fD3d0dcrkcu3btwqRJk7Bjxw5otVoolcoKbRUKBTQaTYVlarXOmOUahbOzA/LztaYuw2AsvX9ExlLd3yNL/937a/9cXZVPaP14ZnPjjo+PDxQKBeRyOUJDQ+Hr64sjR47AwcEBarW6Qlu1Wg1HR0cTVUpERHWF2YTk38lkMgiCAE9PT2SWZ7hDAAAViUlEQVRmZuqX37hxAyUlJWjRooXpiiMiojrBLELyjz/+wNGjR6HT6VBaWoqdO3ciPT0d3bt3x+DBg3Ho0CGkp6dDq9Xi008/Rd++fXnTDhERGZxZfCZZWlqKZcuW4bfffoO1tTVefPFFrFixAi1btgQAzJ8/H9HR0cjPz0fXrl0RGxtr4oqJiKguMIuQdHFxwbZt20TXDx48GIMHDzZiRURERGZyuZWIiMgcmcWZJNVO6zesgUZdKKktRwUhotqIIUlPTaMulDQiCMBRQYiodmJIklFIHYeSiMicMCTJKKSOQwnwrJOIzAdv3CEiIhLBkCQiIhLBkCQiIhLBzySJiGqx6twUx0exqo8hSURUi/GmOMPi5VYiIiIRDEkiIiIRDEkiIiIRDEkiIiIRDEkiIiIRDEkiIiIRDEkiIiIRDEkiIiIRDEkiIiIRDEkiIiIRDEkiIiIRDEkiIiIRDEkiIiIRDEkiIiIRnCqLKlm/YQ006kJTl0FEZHIMSapEoy6UND8d56YjIkvHy61EREQieCZZi1XnsqiVtQ3Ky0oNXBERkWVhSNZiUi+LAg8vjVanLRFZHpmVNVaujJPU1lGhxJsR4w1ckfljSBIR1RFCeZnkP5Z/+WotAxW1JCTz8/MxZ84c/PDDD6hfvz5mzpyJwYMHm7osg+CdpURkDqoTqJZ89alWhOSCBQtga2uLH374ARkZGZg4cSK8vb3h6elp6tJqXHUvoRIRkeGYfUhqtVp8++23SE1NhaOjI/z9/dG7d2/s2LED0dHRNb4/Q90MwxtniMhSSf2sszr/D5rLJVyZIAiCqYt4nF9//RUjR47E2bNn9cvWrl2LU6dOYdWqVSasjIiILJ3ZPyep1WqhUCgqLFMqldBoNCaqiIiI6gqzD0kHBweo1eoKy9RqNRwdHU1UERER1RVmH5ItWrRAWVkZrl69ql+WmZkJDw8P0xVFRER1gtmHpIODA/r27Yvly5dDq9Xip59+woEDBzBkyBBTl0ZERBbO7EMSAGJiYlBUVITAwEDMmjUL8+bNq7WPf+Tn52PKlCno2LEjgoODkZqaWmW7+Ph4tG3bFiqVSv/vxo0b+vVeXl7o2LGjft2cOXOM1QVRUvsGABcuXMAbb7wBlUqFwMBArF+/Xr8uOzsb4eHh8PHxwYABA3D8+HFjlP9ENdW/3r17o0OHDvpjN2bMGGOU/0RS+zdu3LgKP5ft2rWr8NxybT9+T+qfOR4/qX0rLi7Ghx9+iMDAQAQEBGDSpEnIycmp9naMrab6Fx4ejvbt2+uPXf/+/Z+8c4GMasaMGcK0adMEtVotnDp1SvD19RUuXbpUqd3y5cuFWbNmiW6nVatWwtWrVw1ZarVJ7dv9+/eFLl26CDt27BB0Op1QWFgoXLlyRb9++PDhwqJFi4Q///xT2Lt3r+Dn5yfcv3/fmF2pUk31Lzg4WPjhhx+MWbokUvv3d6NGjRLi4+P139f24/d3f++fOR4/qX1bvXq1MHjwYOHevXtCUVGRMHv2bGHKlCnV3o6x1VT/Ro0aJXz11VfV2netOJO0FI+e+Zw2bVqlZz5ru+r0bd26dejWrRteeeUVyOVyKBQKuLu7AwB+//13XLhwAVFRUbC3t0f//v3RqlUr7Nu3z9hdqqCm+meunvZnMzs7G+np6Rg6dCgAyzh+f/X3/pmj6vQtOzsb3bp1Q4MGDWBnZ4dBgwbh8uXL1d6OMdVU/54WQ9KIrl69Cmtra7Rs2VK/zNvbG1euXKmy/aFDhxAQEICXX34ZX3zxRaX1b7zxBoKCghAZGYns7GyD1S1Fdfr2888/w8nJCSNGjEDXrl0xadIk3Lp1CwBw5coVvPDCCxUe+3nce2QsNdW/R6Kjo9GlSxeMGTMGmZmZBq//Sar7s/nI9u3b4e/vj2bNmgGwjOP3V3/v3yPmdPyq07fXXnsNp0+fRk5ODv7880+kpqaiR48e1d6OMdVU/x5ZsmQJOnfujBEjRiAtLe2J+2dIGlF1nvkcOHAgdu/ejRMnTuCjjz7CypUr8c033+jXb9q0CQcPHsSePXvg5uaGSZMmobTUdCP6VKdvOTk52L59O95//30cPnwYzZo1w8yZMwEAGo0GSqVS0naMqab6BwD/+te/cPDgQRw6dAidO3fG2LFj8ccffxi8D4/ztM8j79ixA6GhofrvLeH4/dXf+weY3/GrTt9atGiBxo0bo0ePHvDz80NWVhamTJlS7e0YU031D3j4x813332Ho0eP4p///CcmTZqE69evP3b/DEkjqs4znx4eHmjYsCGsra3h6+uLiIiICpesOnXqBLlcjueeew5z5sxBdnY2srKyDN4HMdXpm52dHfr27YsOHTrAzs4OU6ZMwZkzZ1BYWAhHR0ezfC62pvoHAH5+frC3t0e9evUwceJEKJVKpKenG6UfYp7meeT09HTk5uZWuPnBEo7fI1X1DzC/41edvs2fPx/FxcVIS0vDzz//jL59+2L8+PHV3o4x1VT/AMDHxwcKhQJyuRyhoaHw9fXFkSNHHrt/hqQRPeszn8JjRhCUyWSPXW9o1embl5dXhe9lMpn+aw8PD9y4caPCL4U5PBdbU/2riqmPHfB0P5vbt29H3759K/xnZQnH75Gq+lcVUx+/6vQtMzMToaGhcHZ2hlwuR3h4OM6dO4e8vDyzfSa9pvpXFSnHjiFpRNV55vO7775DQUEBBEHAuXPnsHHjRvTp0wcAcPnyZWRkZKCsrAwajQaLFy+Gm5ubSW8OqU7fhg0bhu+++w4ZGRkoKSnBypUr4efnB6VSiZYtW6J169ZYsWIFdDod9u/fj4sXL0q7VduAaqp/t27dwk8//YTi4mLodDokJibiwYMH8PX1NUGv/qu6zyMXFRVhz549lS5FWsLxA8T7Z47Hrzp9a9++PXbs2IHCwkKUlJTgiy++gJubG1xcXMz2mfSa6t8ff/yBo0ePQqfTobS0FDt37kR6ejq6d+/++AKe4a5cegoPHjwQ3nrrLcHHx0fo2bOnsHPnTkEQBOHUqVNCx44d9e1mzJghBAQECB07dhT69+8vrF+/Xr/u+PHjQr9+/QQfHx+hS5cuwltvvSX8/vvvxu5KJVL7JgiC8PnnnwvdunUT/P39hYkTJwq3bt3Sr7tx44YwatQooX379kK/fv3M5nb7mujfpUuXhJCQEMHHx0cICAgQIiIihHPnzhm9L1WpTv9SU1OFXr16CeXl5ZW2YwnHT6x/5nr8pPYtLy9PmDlzptClSxfBz89PGDFihHD27NknbsfUaqJ/9+/fF4YNGyZ07NhR8PPzE8LCwoRjx449cd9mPwsIERGRqfByKxERkQiGJBERkQiGJBERkQiGJBERkQiGJBERkQiGJBERkQiGJFmE+Ph4REdHP9Vrv/76a4wcOVJ0/bhx45CSklJl27/P82koRUVFmDRpEvz8/DB16lSD78/Urly5gmHDhomOhpKdnQ0vLy+jjVf82muvPfNsElQ7MSTJZP46eW1gYCDeffddkw+mXJXExMRKI688cubMGbzwwgsAgHfffRdLly41SA179+5Fbm4u0tLSsHz5coPsw5x8+umnGDt2rH5Iv969e9fY5M1PE7BjxoypE+87VcaQJJNatWoVzpw5g5SUFPzyyy9ISEio1EYQBJSXl5ugOvNx69YttGjRAjY2NqYuxeDu3r2LtLQ0vPTSS6YuRa9Pnz5IS0vDvXv3TF0KGRlDksxCw4YN0b17d/0lrfDwcCxduhQjRoyAj48Pbty4gZycHEyaNAkBAQHo27cvvvrqqwrbKC4uxvTp06FSqRAaGlphnr/Vq1fjpZdegkqlwqBBg7B///4KrxUEAQsWLICfnx8GDBiAEydO6NeFh4cjOTm5yrq9vLxw7do1bNmyBampqVi7di1UKhUmTZqExMREREVFVWi/cOFCLFy4sMptZWVlITw8HP7+/nj55Zdx4MABAMDy5cuxcuVK7NmzByqVqspazp07h2HDhsHX1xeBgYGIjY0FAKSlpVWaT++vZ2VlZWVYtWqV/r0ZNmwYbt++DeDhGMGjR49GQEAAAgMDsWrVKgBAeXm5/v3s3Lkzpk2bhvz8fACATqdDdHQ0OnfuDH9/f7z66qvIzc0F8PBSdZ8+faBSqdC7d2/s3Lmzyvfh+PHjaNOmDezs7AAAs2fPxq1btzBp0iSoVCqsWbNG3zY1NRW9evVC586dK/yB9bgaR40aBeDhTDoqlQpnzpzB9evXERERgc6dO6Nz586YNWtWhemv7Ozs0LZtWxw7dqzKmsmC1fgge0QSBQcH68f1vHXrljBo0CBh6dKlgiAIwqhRo4SePXsKly5dEkpKSoTi4mLh9ddfF2JiYoSioiLh119/FTp37iwcP35cEARBWL58udCmTRthz549QnFxsZCYmCgEBwcLxcXFgiAIwu7du4U7d+4IZWVlwq5duwQfHx8hJydHEARB2LZtm9C6dWshKSlJKC4uFnbt2iX4+voKDx480Nfy1Vdf6duOGDFC34dWrVoJV69eFQRBEN555x0hLi5Ovy4nJ0fw8fERCgoKBEEQhJKSEqFLly7C+fPnK70XxcXFwksvvSQkJCQIOp1OOH78uNCxY0chKytL379Zs2aJvpfDhw8XUlJSBEEQBLVaLZw5c0YQBEH48ccfhe7du4u+72vWrBFCQkKErKwsoby8XMjIyBDy8vKEwsJCISgoSFi7dq1QVFQkFBYWCj///LMgCIKwbt06ISwsTLh9+7ag0+mEuXPnCjNmzBAEQRA2b94sTJw4UdBqtUJpaalw/vx5obCwUNBoNIJKpdL3JycnR7h06VKVfVm8eLEwb9480ZoF4eH4sK1atRLmzJkj/Pnnn0JGRobQtm1b4cqVK0+s8dFrS0pK9Nu7evWqcOzYMUGn0wn3798XXn/9dWHhwoUVavjoo4+ERYsWiR4Dskw8kySTmjJlCvz9/fH666+jU6dOmDRpkn5daGgoPD09YWNjg9zcXJw+fRrR0dGws7ND69atERYWhh07dujbt23bFgMGDICtrS1Gjx6N4uJinD17FsDDSawbNmwIKysrDBo0CP/4xz9w7tw5/WtdXFzw5ptvwtbWFoMGDULLli1x+PDhZ+qbm5sb/P39sXfvXgDA0aNHUb9+fbRr165S27Nnz0Kr1WLChAmQy+Xo2rUrgoODsWvXLkn7srGxwfXr15GXlwdHR0d07NhR0uuSk5Mxbdo0vPjii5DJZPD29kb9+vVx+PBhNGjQAGPGjIGdnR0UCgV8fHwAAF9++SVmzJiBRo0aQS6XIzIyEvv27UNpaSlsbGyQn5+Pa9euwdraGu3atdNPmGtlZYXLly+jqKgIbm5u8PT0rLKmR/OKShEZGQl7e3t4e3vD29tbf/XgcTVW5R//+AeCgoIgl8vh4uKC0aNH49SpUxXaODo6mnxybDI+y/+Ag8zaihUrEBgYWOW6xo0b67++e/cunJycKsxQ3qRJE/zyyy/67xs1aqT/2srKCg0bNsTdu3cBPJwbMCkpCTdv3gTwcLbzBw8e6Ns3bNiwwryPTZo00b/2WYSGhmLz5s0YPnw4du7cKTrt0N27d9GoUSNYWf3379YmTZogJydH0n4+/vhjLF++HAMHDkSzZs0QGRmJ4ODgJ77uzp07aN68eaXlt2/frnI58PDz0SlTplSo1crKCvfv38eQIUNw584dzJw5E3/88QdeeeUVzJgxAw4ODli6dCk+++wzzJkzB76+vnjnnXeqnN7tueeek3wDV4MGDfRf16tXD1qt9ok1ViU3Nxcff/wx0tPTodFoIAgCnnvuuQptNBpNpWVk+XgmSWbrr6Hl5uaGgoKCCpP53r59Gw0bNtR/f+fOHf3X5eXlyMnJgZubG27evIkPPvgAc+fORVpaGtLT0yudxeTk5FR43OD27dtwc3N76nofeemll3Dx4kVcunQJhw8fxuDBg6t8rZubG+7cuVPhBqW/9+9xWrRogbi4OJw4cQLjx4/H1KlTodVqUa9ePRQVFenblZWVVZiAtlGjRrh+/Xql7TVu3Fj00ZZGjRphzZo1SE9P1/87f/48GjZsCFtbW0RGRmL37t348ssvcfjwYWzfvh0A0L17dyQlJeHYsWN48cUXMXfu3Cq37+XlVWGC3afxuBqrOk5xcXGQyWRITU3F6dOn8a9//avS4ydZWVnw9vZ+prqo9mFIUq3QuHFjqFQqxMXFQafTITMzE1u3bsUrr7yib3PhwgV8++23KC0txfr16yGXy+Hj44M///wTMpkMLi4uAIBt27ZVeuYtLy8PGzZsQElJCfbs2YOsrCz07NmzWjU+//zzyM7OrrDMzs4O/fv3x6xZs9C+fXs0adKkytd26NAB9vb2SExMRElJCdLS0nDw4EEMGjRI0r537NiBvLw8WFlZ6c92rKys0LJlS+h0Ohw+fBglJSVISEhAcXGx/nVhYWH49NNPcfXqVQiCgMzMTDx48AC9evXCvXv3sG7dOhQXF0OtVusvXY8cORLLli3Tn5Xn5eXhu+++AwD8+OOPuHjxIsrKyqBQKGBjYwMrKyvk5ubiu+++g1arhVwuh4ODQ4WzvL8KCgrCr7/+Cp1Op1/WoEGDaj2P+rgaXVxcYGVlVWF7Go0GDg4OUCqVyMnJQWJiYoXt6XQ6XLhwQfSqB1kuhiTVGnFxcbh58ya6d++OyMhIREVFVfhPq0+fPti9ezc6deqEHTt2ID4+Hra2tvDw8MCYMWMwYsQIBAYG4tKlS5Vmku/QoQOuXbuGLl26YNmyZVi+fDnq169frfpee+01XLlyBf7+/pg8ebJ++dChQ3Hp0qXHzvAul8uxatUqfP/99+jSpQvmz5+PTz75pMrLkVU5evQoXn75ZahUKnz88cdYunQp7O3toVQqERMTgw8++AA9evRAvXr1KlyWHj16NAYOHIgxY8bA19cXc+bMgU6ng0KhwGeffYZDhw4hKCgI/fv3R1paGgAgIiICvXv3xpgxY6BSqTB8+HD957u5ubmYOnUq/Pz8MGjQIAQEBGDIkCEoLy/HunXr0L17dwQEBODUqVOYN29elX1p0KABOnfurL+7FwAmTJiAhIQE+Pv7Y+3atU98Px5XY7169TBp0iSMHDkS/v7++PnnnxEZGYlff/0V/v7+mDBhAvr161dhewcPHkRAQIDkM3uyHJx0mcjAbt26hYEDB+KHH36o8Jkqibty5QreeecdbN26tcrLo8YWFhaGjz/+GK1atTJ1KWRkDEkiAyovL0dsbCzUarX+2UUiqj14dyuRgWi1WgQFBaFJkyaVPuMiotqBZ5JEREQieOMOERGRCIYkERGRCIYkERGRCIYkERGRCIYkERGRCIYkERGRiP8Hpi+yni9G9PQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 504x388.8 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 460.8x345.6 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = dict(N=100, y=70)\n",
    "fit = model.sampling(data=data, seed=194838)\n",
    "samples = fit.extract(permuted=True)\n",
    "plt.hist(samples['theta'], 33, color='lightblue', edgecolor='grey') # histogram\n",
    "plt.xlabel(r'Probability of success (theta)')\n",
    "plt.ylabel('Amount of draws')\n",
    "\n",
    "az.plot_posterior(fit, var_names=['theta'], credible_interval=0.95, round_to=2)\n",
    "plt.xlabel(r'Probability of success (theta)')\n",
    "plt.ylabel('Relative density');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explicit transformation of variables\n",
    "In the above examples the probability of success θ was declared as:\n",
    "\n",
    "real<lower=0,upper=1> theta;\n",
    "\n",
    "Stan makes automatic transformation of the variable to the unconstrained space using logit transofrmation for interval constrained and log transformation for half constraints.\n",
    "\n",
    "The following example shows how we can also make an explicit transformation and use binomial_logit function which takes the unconstrained parameter as an argument and uses logit transformation internally. This form can be useful for better numerical stability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "// Binomial model with a roughly uniform prior for\n",
      "// the probability of success (theta)\n",
      "data {\n",
      "  int<lower=0> N;\n",
      "  int<lower=0> y;\n",
      "}\n",
      "parameters {\n",
      "  real alpha;\n",
      "}\n",
      "transformed parameters {\n",
      "  real theta;\n",
      "  theta = inv_logit(alpha);\n",
      "}\n",
      "model {\n",
      "  // roughly auniform prior for the number of successes\n",
      "  alpha ~ normal(0,1.5);\n",
      "  y ~ binomial_logit(N,alpha);\n",
      "}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with open('binomb.stan') as file:\n",
    "    print(file.read())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    }
   ],
   "source": [
    "model = stan_utility.compile_model('binomb.stan')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we have used Gaussian prior in the unconstrained space, which produces close to uniform prior for theta. \n",
    "\n",
    "Sample from the posterior and plot the posterior. The histogram should look similar as with the previous model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x388.8 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 460.8x345.6 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data = dict(N=100, y=70)\n",
    "fit = model.sampling(data=data, seed=194838)\n",
    "samples = fit.extract(permuted=True)\n",
    "plt.hist(samples['theta'], 33, color='lightblue', edgecolor='grey')\n",
    "plt.xlabel(r'Probability of success (theta)')\n",
    "plt.ylabel('Amount of draws')\n",
    "\n",
    "az.plot_posterior(fit, var_names=['theta'], credible_interval=0.95, round_to=2)\n",
    "plt.xlabel(r'Probability of success (theta)')\n",
    "plt.ylabel('Relative density');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparison of two groups with Binomial\n",
    "\n",
    "An experiment was performed to estimate the effect of beta-blockers on mortality of cardiac patients. A group of patients were randomly assigned to treatment and control groups:\n",
    "\n",
    "- out of 674 patients receiving the control, 39 died\n",
    "- out of 680 receiving the treatment, 22 died\n",
    "\n",
    "Data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = dict(N1=674, y1=39, N2=680, y2=22)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To analyse whether the treatment is useful, we can use Binomial model for both groups and compute odds-ratio. If the odds-ratio is less than 1, it means that the treatment is useful."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "//  Comparison of two groups with Binomial\n",
      "data {\n",
      "  int<lower=0> N1;\n",
      "  int<lower=0> y1;\n",
      "  int<lower=0> N2;\n",
      "  int<lower=0> y2;\n",
      "}\n",
      "parameters {\n",
      "  real<lower=0,upper=1> theta1;\n",
      "  real<lower=0,upper=1> theta2;\n",
      "}\n",
      "model {\n",
      "  theta1 ~ beta(1,1);\n",
      "  theta2 ~ beta(1,1);\n",
      "  y1 ~ binomial(N1,theta1);\n",
      "  y2 ~ binomial(N2,theta2);\n",
      "}\n",
      "generated quantities {\n",
      "  real oddsratio;\n",
      "  oddsratio = (theta2/(1-theta2))/(theta1/(1-theta1));\n",
      "}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with open('binom2.stan') as file:\n",
    "    print(file.read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sample from the posterior and plot the posterior for the odds-ratio. We plot the posterior both as a histogram and and as an estimated probability density function. Using ArviZ, we can easily see the probability of the odds-ratio being less than 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x388.8 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 460.8x345.6 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = stan_utility.compile_model('binom2.stan')\n",
    "fit = model.sampling(data=data, seed=194838)\n",
    "samples = fit.extract(permuted=True)\n",
    "plt.hist(samples['oddsratio'], 33, color='lightblue', edgecolor='grey')\n",
    "plt.xlabel('oddsratio')\n",
    "plt.ylabel('Amount of draws')\n",
    "\n",
    "# With az.plot_posterior we use parameter ref_val = 1\n",
    "# since treatment is beneficial if oddsratio is smaller than 1.\n",
    "az.plot_posterior(fit, var_names=['oddsratio'], credible_interval=0.95, round_to=2, ref_val=1)\n",
    "plt.xlabel('oddsratio')\n",
    "plt.ylabel('Relative density')\n",
    "plt.savefig('odd-ratio.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Gaussian model\n",
    "\n",
    "The following file has Kilpisjärvi summer month temperatures 1952-2013:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_path = os.path.abspath(\n",
    "    os.path.join(\n",
    "        os.path.pardir,\n",
    "        'utilities_and_data',\n",
    "        'kilpisjarvi-summer-temp.csv'\n",
    "    )\n",
    ")\n",
    "d = np.loadtxt(data_path, dtype=np.double, delimiter=';', skiprows=1)\n",
    "x = d[:, 0]\n",
    "y = d[:, 4]\n",
    "N = len(x)\n",
    "xpred = 2016"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 705.6x388.8 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make slightly wider figure\n",
    "wide_figsize = plt.rcParams['figure.figsize'].copy()\n",
    "wide_figsize[0] *= 1.4\n",
    "plt.figure(figsize=wide_figsize)\n",
    "plt.scatter(x, y)\n",
    "plt.xlabel('year')\n",
    "plt.ylabel('summer temperature at Kilpisjarvi');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To analyse whether the average summer month temperature is rising, we use a linear model with Gaussian model for the unexplained variation. \n",
    "\n",
    "### Gaussian linear model with adjustable priors\n",
    "\n",
    "The following Stan code allows also setting hyperparameter values as data allowing easier way to use different priors in different analyses:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "// Gaussian linear model with adjustable priors\n",
      "data {\n",
      "  int<lower=0> N; // number of data points\n",
      "  vector[N] x; //\n",
      "  vector[N] y; //\n",
      "  real xpred; // input location for prediction\n",
      "  real pmualpha; // prior mean for alpha\n",
      "  real psalpha;  // prior std for alpha\n",
      "  real pmubeta;  // prior mean for beta\n",
      "  real psbeta;   // prior std for beta\n",
      "}\n",
      "parameters {\n",
      "  real alpha;\n",
      "  real beta;\n",
      "  real<lower=0> sigma;\n",
      "}\n",
      "transformed parameters {\n",
      "  vector[N] mu;\n",
      "  mu = alpha + beta*x;\n",
      "}\n",
      "model {\n",
      "  alpha ~ normal(pmualpha, psalpha);\n",
      "  beta ~ normal(pmubeta, psbeta);\n",
      "  y ~ normal(mu, sigma);\n",
      "}\n",
      "generated quantities {\n",
      "  real ypred;\n",
      "  vector[N] log_lik;\n",
      "  ypred = normal_rng(alpha + beta*xpred, sigma);\n",
      "  for (i in 1:N)\n",
      "    log_lik[i] = normal_lpdf(y[i] | mu[i], sigma);\n",
      "}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with open('lin.stan') as file:\n",
    "    print(file.read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a list with data and priors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = dict(\n",
    "    N = N,\n",
    "    x = x,\n",
    "    y = y,\n",
    "    xpred = xpred,\n",
    "    pmualpha = y.mean(),     # centered\n",
    "    psalpha  = 100,          # weakly informative prior\n",
    "    pmubeta  = 0,            # a priori increase and decrese as likely\n",
    "    psbeta   = (.1--.1)/6.0  # avg temp probably does not increase more than 1\n",
    "                             # degree per 10 years\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run Stan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:pystan:178 of 4000 iterations saturated the maximum tree depth of 10 (4.45%)\n",
      "WARNING:pystan:Run again with max_treedepth larger than 10 to avoid saturation\n"
     ]
    }
   ],
   "source": [
    "model = stan_utility.compile_model('lin.stan')\n",
    "fit_lin = model.sampling(data=data, seed=194838)\n",
    "samples = fit_lin.extract(permuted=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the `n_eff` and `Rhat`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inference for Stan model: anon_model_6d95d5cbf9b9fb7d99a793b066a7bb72.\n",
      "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
      "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
      "\n",
      "              mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
      "alpha       -28.09    0.47  16.09 -59.57  -39.0 -27.89  -17.1   3.04   1172    1.0\n",
      "beta          0.02  2.4e-4 8.1e-3 3.2e-3   0.01   0.02   0.02   0.03   1172    1.0\n",
      "sigma         1.13  3.0e-3   0.11   0.94   1.05   1.13    1.2   1.38   1452    1.0\n",
      "mu[1]         8.74  7.7e-3   0.29   8.17   8.54   8.74   8.93    9.3   1417    1.0\n",
      "mu[2]         8.75  7.4e-3   0.28   8.21   8.56   8.76   8.95    9.3   1432    1.0\n",
      "mu[3]         8.77  7.2e-3   0.27   8.24   8.58   8.77   8.96   9.31   1448    1.0\n",
      "mu[4]         8.79  7.0e-3   0.27   8.27   8.61   8.79   8.97   9.31   1466    1.0\n",
      "mu[5]         8.81  6.8e-3   0.26   8.31   8.63   8.81   8.99   9.32   1485    1.0\n",
      "mu[6]         8.83  6.6e-3   0.25   8.34   8.66   8.83    9.0   9.32   1509    1.0\n",
      "mu[7]         8.85  6.3e-3   0.25   8.37   8.68   8.85   9.02   9.32   1533    1.0\n",
      "mu[8]         8.87  6.1e-3   0.24    8.4    8.7   8.87   9.03   9.33   1559    1.0\n",
      "mu[9]         8.89  5.9e-3   0.24   8.43   8.73   8.89   9.05   9.34   1588    1.0\n",
      "mu[10]        8.91  5.7e-3   0.23   8.46   8.75   8.91   9.06   9.35   1620    1.0\n",
      "mu[11]        8.92  5.5e-3   0.22   8.49   8.77   8.93   9.07   9.36   1655    1.0\n",
      "mu[12]        8.94  5.3e-3   0.22   8.52    8.8   8.94   9.09   9.36   1695    1.0\n",
      "mu[13]        8.96  5.1e-3   0.21   8.56   8.82   8.96    9.1   9.37   1740    1.0\n",
      "mu[14]        8.98  4.8e-3    0.2   8.58   8.84   8.98   9.12   9.38   1790    1.0\n",
      "mu[15]         9.0  4.6e-3    0.2   8.61   8.86    9.0   9.13   9.39   1846    1.0\n",
      "mu[16]        9.02  4.4e-3   0.19   8.64   8.89   9.02   9.15    9.4   1910    1.0\n",
      "mu[17]        9.04  4.2e-3   0.19   8.67   8.91   9.04   9.16   9.41   1986    1.0\n",
      "mu[18]        9.06  4.0e-3   0.18    8.7   8.93   9.06   9.18   9.42   2076    1.0\n",
      "mu[19]        9.07  3.8e-3   0.18   8.73   8.95   9.08    9.2   9.43   2178    1.0\n",
      "mu[20]        9.09  3.6e-3   0.17   8.75   8.98   9.09   9.21   9.44   2294    1.0\n",
      "mu[21]        9.11  3.5e-3   0.17   8.78    9.0   9.11   9.23   9.45   2425    1.0\n",
      "mu[22]        9.13  3.3e-3   0.17    8.8   9.02   9.13   9.24   9.46   2573    1.0\n",
      "mu[23]        9.15  3.1e-3   0.16   8.83   9.04   9.15   9.26   9.47   2739    1.0\n",
      "mu[24]        9.17  2.9e-3   0.16   8.85   9.06   9.17   9.28   9.48   2921    1.0\n",
      "mu[25]        9.19  2.8e-3   0.16   8.88   9.08   9.19   9.29   9.49   3123    1.0\n",
      "mu[26]        9.21  2.7e-3   0.15    8.9    9.1   9.21   9.31   9.51   3296    1.0\n",
      "mu[27]        9.23  2.6e-3   0.15   8.92   9.12   9.23   9.33   9.52   3462    1.0\n",
      "mu[28]        9.24  2.5e-3   0.15   8.95   9.14   9.24   9.34   9.54   3617    1.0\n",
      "mu[29]        9.26  2.4e-3   0.15   8.97   9.16   9.26   9.36   9.55   3753    1.0\n",
      "mu[30]        9.28  2.4e-3   0.15    9.0   9.18   9.28   9.38   9.57   3856    1.0\n",
      "mu[31]         9.3  2.3e-3   0.15   9.01    9.2    9.3    9.4   9.59   3919    1.0\n",
      "mu[32]        9.32  2.3e-3   0.15   9.03   9.22   9.32   9.42   9.61   3934    1.0\n",
      "mu[33]        9.34  2.3e-3   0.15   9.05   9.24   9.34   9.44   9.63   3900    1.0\n",
      "mu[34]        9.36  2.4e-3   0.15   9.07   9.26   9.36   9.46   9.65   3820    1.0\n",
      "mu[35]        9.38  2.4e-3   0.15   9.08   9.28   9.37   9.48   9.67   3704    1.0\n",
      "mu[36]         9.4  2.5e-3   0.15    9.1    9.3   9.39    9.5   9.69   3560    1.0\n",
      "mu[37]        9.41  2.6e-3   0.15   9.11   9.32   9.41   9.52   9.71   3377    1.0\n",
      "mu[38]        9.43  2.7e-3   0.16   9.12   9.33   9.43   9.54   9.74   3189    1.0\n",
      "mu[39]        9.45  2.9e-3   0.16   9.13   9.35   9.45   9.56   9.76   3006    1.0\n",
      "mu[40]        9.47  3.0e-3   0.16   9.15   9.37   9.47   9.58   9.79   2834    1.0\n",
      "mu[41]        9.49  3.2e-3   0.16   9.16   9.38   9.49    9.6   9.81   2675    1.0\n",
      "mu[42]        9.51  3.4e-3   0.17   9.17    9.4   9.51   9.62   9.84   2530    1.0\n",
      "mu[43]        9.53  3.5e-3   0.17   9.18   9.42   9.53   9.64   9.86   2400    1.0\n",
      "mu[44]        9.55  3.7e-3   0.18   9.19   9.43   9.55   9.66   9.89   2284    1.0\n",
      "mu[45]        9.57  3.9e-3   0.18    9.2   9.45   9.57   9.68   9.92   2181    1.0\n",
      "mu[46]        9.58  4.1e-3   0.19   9.21   9.46   9.58    9.7   9.95   2089    1.0\n",
      "mu[47]         9.6  4.3e-3   0.19   9.22   9.48    9.6   9.73   9.97   2005    1.0\n",
      "mu[48]        9.62  4.5e-3    0.2   9.23   9.49   9.62   9.75  10.01   1932    1.0\n",
      "mu[49]        9.64  4.7e-3    0.2   9.24   9.51   9.64   9.77  10.04   1869    1.0\n",
      "mu[50]        9.66  4.9e-3   0.21   9.25   9.52   9.66    9.8  10.07   1811    1.0\n",
      "mu[51]        9.68  5.1e-3   0.21   9.25   9.54   9.68   9.82   10.1   1760    1.0\n",
      "mu[52]         9.7  5.3e-3   0.22   9.26   9.55    9.7   9.84  10.13   1714    1.0\n",
      "mu[53]        9.72  5.5e-3   0.23   9.27   9.57   9.72   9.87  10.16   1673    1.0\n",
      "mu[54]        9.74  5.8e-3   0.23   9.28   9.58   9.74   9.89  10.19   1636    1.0\n",
      "mu[55]        9.75  6.0e-3   0.24   9.29    9.6   9.75   9.91  10.22   1603    1.0\n",
      "mu[56]        9.77  6.2e-3   0.25    9.3   9.61   9.77   9.94  10.25   1573    1.0\n",
      "mu[57]        9.79  6.4e-3   0.25    9.3   9.62   9.79   9.96  10.28   1546    1.0\n",
      "mu[58]        9.81  6.6e-3   0.26   9.31   9.64   9.81   9.98  10.31   1521    1.0\n",
      "mu[59]        9.83  6.9e-3   0.27   9.31   9.65   9.83  10.01  10.35   1499    1.0\n",
      "mu[60]        9.85  7.1e-3   0.27   9.32   9.66   9.85  10.03  10.38   1479    1.0\n",
      "mu[61]        9.87  7.3e-3   0.28   9.33   9.68   9.87  10.05  10.41   1460    1.0\n",
      "mu[62]        9.89  7.5e-3   0.29   9.33   9.69   9.89  10.08  10.45   1444    1.0\n",
      "ypred         9.96    0.02   1.17   7.64   9.18   9.96  10.73  12.25   3522    1.0\n",
      "log_lik[1]   -1.15  3.7e-3   0.13  -1.45  -1.23  -1.14  -1.05  -0.92   1334    1.0\n",
      "log_lik[2]   -2.91    0.01   0.54  -4.13  -3.24  -2.85  -2.52   -2.0   1447    1.0\n",
      "log_lik[3]   -1.23  4.1e-3   0.16  -1.58  -1.32  -1.21  -1.11  -0.96   1489    1.0\n",
      "log_lik[4]   -1.26  4.3e-3   0.16  -1.62  -1.36  -1.25  -1.14  -0.99   1415    1.0\n",
      "log_lik[5]   -1.27  4.3e-3   0.16  -1.63  -1.37  -1.26  -1.15   -1.0   1437    1.0\n",
      "log_lik[6]   -1.58  6.0e-3   0.23  -2.09  -1.72  -1.55  -1.41  -1.19   1522    1.0\n",
      "log_lik[7]   -1.09  2.9e-3   0.11  -1.32  -1.16  -1.09  -1.01  -0.89   1412    1.0\n",
      "log_lik[8]   -1.08  2.9e-3   0.11   -1.3  -1.15  -1.08  -1.01  -0.89   1451    1.0\n",
      "log_lik[9]   -2.85    0.01   0.46  -3.89  -3.13   -2.8  -2.51  -2.06   1547    1.0\n",
      "log_lik[10]  -1.63  5.4e-3   0.22  -2.13  -1.77  -1.61  -1.47  -1.27   1640    1.0\n",
      "log_lik[11]  -1.76  5.9e-3   0.24  -2.29  -1.91  -1.74  -1.59  -1.36   1690    1.0\n",
      "log_lik[12]  -1.07  2.7e-3    0.1  -1.27  -1.13  -1.06   -1.0  -0.88   1444    1.0\n",
      "log_lik[13]  -1.23  3.2e-3   0.13  -1.51  -1.31  -1.22  -1.14  -1.01   1628    1.0\n",
      "log_lik[14]  -2.33  8.0e-3   0.33  -3.06  -2.53  -2.29  -2.09  -1.79   1736    1.0\n",
      "log_lik[15]  -1.09  2.7e-3   0.11  -1.31  -1.16  -1.09  -1.02   -0.9   1501    1.0\n",
      "log_lik[16]  -1.07  2.6e-3    0.1  -1.28  -1.14  -1.07   -1.0  -0.89   1487    1.0\n",
      "log_lik[17]  -1.88  5.1e-3   0.23  -2.37  -2.02  -1.86  -1.72   -1.5   1968    1.0\n",
      "log_lik[18]  -1.89  4.9e-3   0.22  -2.37  -2.02  -1.87  -1.73  -1.51   1964    1.0\n",
      "log_lik[19]  -2.53  7.6e-3   0.33  -3.25  -2.73   -2.5   -2.3  -1.97   1864    1.0\n",
      "log_lik[20]  -1.07  2.6e-3    0.1  -1.27  -1.13  -1.07   -1.0  -0.89   1491    1.0\n",
      "log_lik[21]  -2.96  9.2e-3    0.4   -3.8  -3.21  -2.93  -2.68  -2.28   1858    1.0\n",
      "log_lik[22]  -1.35  2.6e-3   0.12  -1.61  -1.43  -1.35  -1.27  -1.13   2279    1.0\n",
      "log_lik[23]  -1.41  2.5e-3   0.13  -1.68  -1.49  -1.41  -1.32  -1.18   2503    1.0\n",
      "log_lik[24]  -4.12    0.01   0.62  -5.47   -4.5  -4.05  -3.68  -3.06   1712    1.0\n",
      "log_lik[25]  -1.44  2.3e-3   0.12  -1.71  -1.52  -1.43  -1.36  -1.22   3027    1.0\n",
      "log_lik[26]  -1.31  2.1e-3   0.11  -1.54  -1.38  -1.31  -1.24  -1.11   2745    1.0\n",
      "log_lik[27]  -1.08  2.6e-3    0.1  -1.29  -1.14  -1.08  -1.01  -0.89   1510    1.0\n",
      "log_lik[28]  -1.22  2.3e-3    0.1  -1.43  -1.29  -1.22  -1.15  -1.02   2079    1.0\n",
      "log_lik[29]  -1.76  2.7e-3   0.16   -2.1  -1.86  -1.75  -1.65  -1.48   3497    1.0\n",
      "log_lik[30]  -2.18  4.7e-3   0.24   -2.7  -2.33  -2.16  -2.01  -1.78   2529    1.0\n",
      "log_lik[31]  -2.07  4.1e-3   0.22  -2.56  -2.21  -2.06  -1.92  -1.71   2702    1.0\n",
      "log_lik[32]  -1.64  2.3e-3   0.14  -1.95  -1.73  -1.63  -1.54  -1.39   3754    1.0\n",
      "log_lik[33]   -1.4  1.9e-3   0.11  -1.64  -1.47  -1.39  -1.32   -1.2   3612    1.0\n",
      "log_lik[34]   -1.1  2.5e-3    0.1   -1.3  -1.16  -1.09  -1.03  -0.91   1559    1.0\n",
      "log_lik[35]  -1.05  2.6e-3    0.1  -1.26  -1.12  -1.05  -0.99  -0.87   1442    1.0\n",
      "log_lik[36]  -2.81  7.9e-3   0.35  -3.61  -3.02  -2.77  -2.56   -2.2   2010    1.0\n",
      "log_lik[37]  -1.36  2.2e-3   0.11   -1.6  -1.43  -1.36  -1.28  -1.15   2709    1.0\n",
      "log_lik[38]  -1.06  2.6e-3    0.1  -1.26  -1.12  -1.06  -0.99  -0.88   1450    1.0\n",
      "log_lik[39]  -1.34  2.3e-3   0.12  -1.58  -1.41  -1.33  -1.26  -1.12   2430    1.0\n",
      "log_lik[40]  -1.09  2.6e-3    0.1   -1.3  -1.16  -1.09  -1.02  -0.91   1529    1.0\n",
      "log_lik[41]  -1.15  2.4e-3    0.1  -1.35  -1.21  -1.14  -1.08  -0.96   1792    1.0\n",
      "log_lik[42]  -1.12  2.5e-3    0.1  -1.32  -1.19  -1.11  -1.05  -0.93   1667    1.0\n",
      "log_lik[43]  -1.05  2.6e-3    0.1  -1.26  -1.11  -1.05  -0.98  -0.87   1427    1.0\n",
      "log_lik[44]  -1.34  2.7e-3   0.13  -1.61  -1.42  -1.33  -1.25  -1.11   2177    1.0\n",
      "log_lik[45]   -1.1  2.7e-3    0.1  -1.31  -1.16  -1.09  -1.03   -0.9   1505    1.0\n",
      "log_lik[46]  -1.39  3.2e-3   0.14  -1.69  -1.47  -1.38  -1.29  -1.14   1976    1.0\n",
      "log_lik[47]  -1.07  2.6e-3    0.1  -1.28  -1.14  -1.07   -1.0  -0.88   1471    1.0\n",
      "log_lik[48]  -1.21  2.8e-3   0.12  -1.46  -1.29   -1.2  -1.13   -1.0   1754    1.0\n",
      "log_lik[49]  -1.22  2.9e-3   0.12  -1.48   -1.3  -1.21  -1.13   -1.0   1733    1.0\n",
      "log_lik[50]  -1.06  2.7e-3    0.1  -1.27  -1.12  -1.06  -0.99  -0.87   1404    1.0\n",
      "log_lik[51]  -2.24  7.6e-3   0.32  -2.94  -2.44  -2.22  -2.01   -1.7   1750    1.0\n",
      "log_lik[52]  -1.46  4.3e-3   0.18  -1.85  -1.56  -1.44  -1.34  -1.16   1699    1.0\n",
      "log_lik[53]  -1.12  3.0e-3   0.11  -1.36  -1.19  -1.11  -1.04  -0.91   1457    1.0\n",
      "log_lik[54]  -1.51  4.9e-3    0.2  -1.96  -1.63   -1.5  -1.38  -1.18   1636    1.0\n",
      "log_lik[55]  -1.23  3.7e-3   0.14  -1.55  -1.32  -1.22  -1.13  -0.98   1508    1.0\n",
      "log_lik[56]  -1.17  3.5e-3   0.13  -1.46  -1.25  -1.16  -1.08  -0.94   1456    1.0\n",
      "log_lik[57]  -1.46  5.1e-3    0.2  -1.92  -1.58  -1.44  -1.32  -1.13   1554    1.0\n",
      "log_lik[58]  -1.07  2.8e-3    0.1  -1.29  -1.13  -1.06  -0.99  -0.88   1366    1.0\n",
      "log_lik[59]  -1.49  5.7e-3   0.22   -2.0  -1.62  -1.47  -1.34  -1.13   1507    1.0\n",
      "log_lik[60]  -1.43  5.5e-3   0.21  -1.92  -1.55  -1.41  -1.28  -1.09   1468    1.0\n",
      "log_lik[61]  -1.71  7.4e-3   0.28  -2.36  -1.88  -1.68  -1.51  -1.25   1467    1.0\n",
      "log_lik[62]  -1.66  7.3e-3   0.28  -2.29  -1.82  -1.63  -1.46  -1.21   1460    1.0\n",
      "lp__        -38.17    0.05   1.35 -41.73 -38.77 -37.82 -37.19 -36.64    902   1.01\n",
      "\n",
      "Samples were drawn using NUTS at Wed Dec 19 11:19:39 2018.\n",
      "For each parameter, n_eff is a crude measure of effective sample size,\n",
      "and Rhat is the potential scale reduction factor on split chains (at \n",
      "convergence, Rhat=1).\n"
     ]
    }
   ],
   "source": [
    "print(fit_lin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Check the treedepth, E-BFMI, and divergences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "178 of 4000 iterations saturated the maximum tree depth of 10 (4.45%)\n",
      "Run again with max_depth set to a larger value to avoid saturation\n",
      "0.0 of 4000 iterations ended with a divergence (0.0%)\n"
     ]
    }
   ],
   "source": [
    "stan_utility.check_treedepth(fit_lin)\n",
    "stan_utility.check_energy(fit_lin)\n",
    "stan_utility.check_div(fit_lin)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get a warning that several iterations saturated the maximum treedepth. The reason for this is a very strong posterior correlation between alpha and beta as shown in the next plot. This doesn't invalidate the results, but leads to suboptimal performance. We'll later look at alternative which reduces the posterior correlation. The following figure shows the strong posterior correlation in the current case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x388.8 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples = fit_lin.extract(permuted=True)\n",
    "# preview 500 posterior samples of (alpha, beta)\n",
    "plt.scatter(samples['alpha'][:500], samples['beta'][:500], 50, marker='.', alpha=0.25)\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('beta');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the probability that the summer temperature is increasing. The beta-parameter represents the slope of the temperature change. Hence, by checking the probability that beta > 0, we get the probability that the temperature is rising."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pr(beta > 0) = 0.9895\n"
     ]
    }
   ],
   "source": [
    "print('Pr(beta > 0) = {}'.format(np.mean(samples['beta'] > 0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the data, the model fit and prediction for year 2016."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1108.8x466.56 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1382.4x345.6 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make slightly wider figure of 3 plots\n",
    "figsize = plt.rcParams['figure.figsize'].copy()\n",
    "figsize[0] *= 2.2  # width\n",
    "figsize[1] *= 1.2  # width\n",
    "fig, ax = plt.subplots(1, 1, figsize=figsize)\n",
    "\n",
    "# plot 1: scatterplot and lines\n",
    "color_scatter = 'C0'  # 'C0' for default color #0\n",
    "color_line = 'C3'     # 'C1' for default color #1\n",
    "\n",
    "ax.fill_between(\n",
    "    x,\n",
    "    np.percentile(samples['mu'], 5, axis=0),\n",
    "    np.percentile(samples['mu'], 95, axis=0),\n",
    "    # lighten color_line\n",
    "    color=1 - 0.4*(1 - np.array(mpl.colors.to_rgb(color_line)))\n",
    ")\n",
    "ax.plot(\n",
    "    x,\n",
    "    np.percentile(samples['mu'], 50, axis=0),\n",
    "    color=color_line,\n",
    "    linewidth=2,\n",
    "    alpha=0.8\n",
    ")\n",
    "ax.scatter(x, y, 10, color=color_scatter)\n",
    "ax.set_xlabel('year')\n",
    "ax.set_ylabel('summer temp. @Kilpisjarvi')\n",
    "ax.set_xlim((1951.5, 2013.5))\n",
    "\n",
    "\n",
    "az.plot_posterior(fit_lin, var_names=['beta','sigma','ypred'], credible_interval=0.95, round_to=2, kind='hist', bins=35)\n",
    "plt.xlabel('y-prediction for x={}'.format(xpred));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the beta parameter (the slope), let's also plot the relative density with reference value of 0. Now we can easily evaluate the probability for slope being positive."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 460.8x345.6 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_posterior(fit_lin, var_names=['beta'], credible_interval=0.95, round_to=2, ref_val=0, kind='kde')\n",
    "plt.xlabel('beta')\n",
    "plt.ylabel('Relative density');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian linear model with standardized data\n",
    "\n",
    "In the above we used the unnormalized data and as x values are far away from zero, this will cause very strong posterior dependency between alpha and beta. The strong posterior dependency can be removed by normalizing the data to have zero mean. The following Stan code makes it in Stan. In generated quantities we do correspnding transformation back to the original scale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "// Gaussian linear model with standardized data\n",
      "data {\n",
      "  int<lower=0> N; // number of data points\n",
      "  vector[N] x; //\n",
      "  vector[N] y; //\n",
      "  real xpred; // input location for prediction\n",
      "}\n",
      "transformed data {\n",
      "  vector[N] x_std;\n",
      "  vector[N] y_std;\n",
      "  real xpred_std;\n",
      "  x_std = (x - mean(x)) / sd(x);\n",
      "  y_std = (y - mean(y)) / sd(y);\n",
      "  xpred_std = (xpred - mean(x)) / sd(x);\n",
      "}\n",
      "parameters {\n",
      "  real alpha;\n",
      "  real beta;\n",
      "  real<lower=0> sigma_std;\n",
      "}\n",
      "transformed parameters {\n",
      "  vector[N] mu_std;\n",
      "  mu_std = alpha + beta*x_std;\n",
      "}\n",
      "model {\n",
      "  alpha ~ normal(0, 1);\n",
      "  beta ~ normal(0, 1);\n",
      "  y_std ~ normal(mu_std, sigma_std);\n",
      "}\n",
      "generated quantities {\n",
      "  vector[N] mu;\n",
      "  real<lower=0> sigma;\n",
      "  real ypred;\n",
      "  vector[N] log_lik;\n",
      "  mu = mu_std*sd(y) + mean(y);\n",
      "  sigma = sigma_std*sd(y);\n",
      "  ypred = normal_rng((alpha + beta*xpred_std)*sd(y)+mean(y), sigma*sd(y));\n",
      "  for (i in 1:N)\n",
      "    log_lik[i] = normal_lpdf(y[i] | mu[i], sigma);\n",
      "}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with open('lin_std.stan') as file:\n",
    "    print(file.read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Run Stan"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    }
   ],
   "source": [
    "model = stan_utility.compile_model('lin_std.stan')\n",
    "fit_lin_std = model.sampling(data=data, seed=194838)\n",
    "samples = fit_lin_std.extract(permuted=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the `n_eff` and `Rhat`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inference for Stan model: anon_model_161eb30961f09398a0825482beb4b070.\n",
      "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
      "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
      "\n",
      "              mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
      "alpha       6.7e-4  2.0e-3   0.12  -0.25  -0.08 1.2e-3   0.08   0.26   3733    1.0\n",
      "beta          0.31  1.9e-3   0.12   0.06   0.23   0.31   0.39   0.55   3988    1.0\n",
      "sigma_std     0.98  1.6e-3   0.09   0.82   0.91   0.97   1.03   1.18   3457    1.0\n",
      "mu_std[1]    -0.52  3.7e-3   0.24  -0.99  -0.68  -0.53  -0.37  -0.04   4221    1.0\n",
      "mu_std[2]    -0.51  3.6e-3   0.23  -0.96  -0.66  -0.51  -0.36  -0.03   4222    1.0\n",
      "mu_std[3]    -0.49  3.5e-3   0.23  -0.93  -0.64  -0.49  -0.34  -0.03   4220    1.0\n",
      "mu_std[4]    -0.47  3.4e-3   0.22  -0.91  -0.62  -0.48  -0.33  -0.02   4216    1.0\n",
      "mu_std[5]    -0.45  3.3e-3   0.22  -0.88   -0.6  -0.46  -0.32  -0.02   4213    1.0\n",
      "mu_std[6]    -0.44  3.2e-3   0.21  -0.85  -0.58  -0.44   -0.3-8.6e-3   4209    1.0\n",
      "mu_std[7]    -0.42  3.2e-3   0.21  -0.82  -0.56  -0.42  -0.29-2.6e-3   4204    1.0\n",
      "mu_std[8]     -0.4  3.1e-3    0.2   -0.8  -0.53  -0.41  -0.28 1.5e-3   4199    1.0\n",
      "mu_std[9]    -0.39  3.0e-3   0.19  -0.77  -0.51  -0.39  -0.26 7.8e-3   4193    1.0\n",
      "mu_std[10]   -0.37  2.9e-3   0.19  -0.74  -0.49  -0.37  -0.25   0.01   4186    1.0\n",
      "mu_std[11]   -0.35  2.8e-3   0.18  -0.71  -0.47  -0.35  -0.23   0.02   4178    1.0\n",
      "mu_std[12]   -0.33  2.8e-3   0.18  -0.69  -0.45  -0.34  -0.22   0.03   4170    1.0\n",
      "mu_std[13]   -0.32  2.7e-3   0.17  -0.66  -0.43  -0.32   -0.2   0.04   4160    1.0\n",
      "mu_std[14]    -0.3  2.6e-3   0.17  -0.64  -0.41   -0.3  -0.19   0.05   4150    1.0\n",
      "mu_std[15]   -0.28  2.6e-3   0.17  -0.61  -0.39  -0.29  -0.18   0.05   4138    1.0\n",
      "mu_std[16]   -0.27  2.5e-3   0.16  -0.58  -0.37  -0.27  -0.16   0.06   4125    1.0\n",
      "mu_std[17]   -0.25  2.4e-3   0.16  -0.56  -0.35  -0.25  -0.15   0.07   4111    1.0\n",
      "mu_std[18]   -0.23  2.4e-3   0.15  -0.53  -0.33  -0.23  -0.13   0.08   4096    1.0\n",
      "mu_std[19]   -0.21  2.3e-3   0.15  -0.51  -0.31  -0.22  -0.12   0.08   4080    1.0\n",
      "mu_std[20]    -0.2  2.3e-3   0.14  -0.48  -0.29   -0.2   -0.1   0.09   4062    1.0\n",
      "mu_std[21]   -0.18  2.2e-3   0.14  -0.46  -0.27  -0.18  -0.09    0.1   4043    1.0\n",
      "mu_std[22]   -0.16  2.2e-3   0.14  -0.43  -0.25  -0.16  -0.07   0.11   4023    1.0\n",
      "mu_std[23]   -0.15  2.1e-3   0.14  -0.41  -0.23  -0.15  -0.06   0.13   4002    1.0\n",
      "mu_std[24]   -0.13  2.1e-3   0.13  -0.39  -0.21  -0.13  -0.04   0.14   3980    1.0\n",
      "mu_std[25]   -0.11  2.1e-3   0.13  -0.37   -0.2  -0.11  -0.03   0.15   3951    1.0\n",
      "mu_std[26]   -0.09  2.1e-3   0.13  -0.35  -0.18   -0.1-9.4e-3   0.16   3918    1.0\n",
      "mu_std[27]   -0.08  2.0e-3   0.13  -0.33  -0.16  -0.08 6.8e-3   0.18   3884    1.0\n",
      "mu_std[28]   -0.06  2.0e-3   0.13  -0.31  -0.14  -0.06   0.02   0.19   3849    1.0\n",
      "mu_std[29]   -0.04  2.0e-3   0.12  -0.29  -0.12  -0.04   0.04   0.21   3815    1.0\n",
      "mu_std[30]   -0.03  2.0e-3   0.12  -0.27  -0.11  -0.03   0.06   0.23   3781    1.0\n",
      "mu_std[31] -7.9e-3  2.0e-3   0.12  -0.26  -0.09-7.5e-3   0.07   0.25   3749    1.0\n",
      "mu_std[32]  9.3e-3  2.0e-3   0.12  -0.24  -0.07 9.9e-3   0.09   0.26   3718    1.0\n",
      "mu_std[33]    0.03  2.1e-3   0.13  -0.22  -0.06   0.03   0.11   0.28   3690    1.0\n",
      "mu_std[34]    0.04  2.1e-3   0.13  -0.21  -0.04   0.05   0.13    0.3   3665    1.0\n",
      "mu_std[35]    0.06  2.1e-3   0.13  -0.19  -0.02   0.06   0.15   0.32   3643    1.0\n",
      "mu_std[36]    0.08  2.1e-3   0.13  -0.18-8.8e-3   0.08   0.16   0.33   3623    1.0\n",
      "mu_std[37]     0.1  2.2e-3   0.13  -0.17 5.9e-3    0.1   0.18   0.36   3607    1.0\n",
      "mu_std[38]    0.11  2.2e-3   0.13  -0.15   0.02   0.11    0.2   0.38   3593    1.0\n",
      "mu_std[39]    0.13  2.3e-3   0.14  -0.14   0.04   0.13   0.22    0.4   3583    1.0\n",
      "mu_std[40]    0.15  2.3e-3   0.14  -0.13   0.05   0.15   0.24   0.43   3575    1.0\n",
      "mu_std[41]    0.16  2.4e-3   0.14  -0.12   0.07   0.16   0.26   0.45   3565    1.0\n",
      "mu_std[42]    0.18  2.4e-3   0.15   -0.1   0.08   0.18   0.28   0.47   3558    1.0\n",
      "mu_std[43]     0.2  2.5e-3   0.15   -0.1    0.1    0.2    0.3    0.5   3553    1.0\n",
      "mu_std[44]    0.22  2.6e-3   0.15  -0.09   0.11   0.22   0.32   0.52   3550    1.0\n",
      "mu_std[45]    0.23  2.6e-3   0.16  -0.08   0.12   0.23   0.34   0.55   3549    1.0\n",
      "mu_std[46]    0.25  2.7e-3   0.16  -0.07   0.14   0.25   0.36   0.57   3550    1.0\n",
      "mu_std[47]    0.27  2.8e-3   0.17  -0.06   0.16   0.27   0.38    0.6   3552    1.0\n",
      "mu_std[48]    0.28  2.9e-3   0.17  -0.05   0.17   0.28    0.4   0.62   3555    1.0\n",
      "mu_std[49]     0.3  2.9e-3   0.17  -0.04   0.18    0.3   0.42   0.65   3559    1.0\n",
      "mu_std[50]    0.32  3.0e-3   0.18  -0.03    0.2   0.32   0.44   0.67   3563    1.0\n",
      "mu_std[51]    0.34  3.1e-3   0.18  -0.03   0.21   0.33   0.46    0.7   3569    1.0\n",
      "mu_std[52]    0.35  3.2e-3   0.19  -0.02   0.23   0.35   0.48   0.73   3575    1.0\n",
      "mu_std[53]    0.37  3.3e-3    0.2  -0.02   0.24   0.37    0.5   0.75   3581    1.0\n",
      "mu_std[54]    0.39  3.3e-3    0.2  -0.01   0.25   0.39   0.52   0.78   3587    1.0\n",
      "mu_std[55]     0.4  3.4e-3   0.21-6.5e-3   0.27    0.4   0.54   0.81   3594    1.0\n",
      "mu_std[56]    0.42  3.5e-3   0.21-3.5e-4   0.28   0.42   0.56   0.84   3601    1.0\n",
      "mu_std[57]    0.44  3.6e-3   0.22 9.2e-3   0.29   0.44   0.58   0.87   3608    1.0\n",
      "mu_std[58]    0.46  3.7e-3   0.22   0.02   0.31   0.45   0.61   0.89   3615    1.0\n",
      "mu_std[59]    0.47  3.8e-3   0.23   0.02   0.32   0.47   0.63   0.92   3622    1.0\n",
      "mu_std[60]    0.49  3.9e-3   0.23   0.03   0.34   0.49   0.65   0.95   3628    1.0\n",
      "mu_std[61]    0.51  4.0e-3   0.24   0.03   0.35   0.51   0.67   0.98   3635    1.0\n",
      "mu_std[62]    0.53  4.1e-3   0.25   0.04   0.36   0.52   0.69   1.01   3642    1.0\n",
      "mu[1]         8.71  4.3e-3   0.28   8.17   8.53    8.7   8.88   9.27   4221    1.0\n",
      "mu[2]         8.73  4.2e-3   0.27    8.2   8.55   8.72    8.9   9.27   4222    1.0\n",
      "mu[3]         8.75  4.1e-3   0.26   8.23   8.57   8.74   8.91   9.28   4220    1.0\n",
      "mu[4]         8.77  4.0e-3   0.26   8.26    8.6   8.76   8.93   9.29   4216    1.0\n",
      "mu[5]         8.79  3.9e-3   0.25   8.29   8.62   8.78   8.95   9.29   4213    1.0\n",
      "mu[6]         8.81  3.8e-3   0.24   8.33   8.64    8.8   8.96    9.3   4209    1.0\n",
      "mu[7]         8.83  3.7e-3   0.24   8.36   8.67   8.82   8.98   9.31   4204    1.0\n",
      "mu[8]         8.85  3.6e-3   0.23   8.39   8.69   8.84   8.99   9.31   4199    1.0\n",
      "mu[9]         8.87  3.5e-3   0.23   8.42   8.72   8.86   9.01   9.32   4193    1.0\n",
      "mu[10]        8.89  3.4e-3   0.22   8.45   8.74   8.88   9.03   9.33   4186    1.0\n",
      "mu[11]        8.91  3.3e-3   0.21   8.49   8.77    8.9   9.04   9.34   4178    1.0\n",
      "mu[12]        8.92  3.2e-3   0.21   8.51   8.79   8.92   9.06   9.35   4170    1.0\n",
      "mu[13]        8.94  3.1e-3    0.2   8.54   8.81   8.94   9.08   9.36   4160    1.0\n",
      "mu[14]        8.96  3.1e-3    0.2   8.58   8.84   8.96   9.09   9.37   4150    1.0\n",
      "mu[15]        8.98  3.0e-3   0.19   8.61   8.86   8.98   9.11   9.37   4138    1.0\n",
      "mu[16]         9.0  2.9e-3   0.19   8.64   8.88    9.0   9.12   9.38   4125    1.0\n",
      "mu[17]        9.02  2.8e-3   0.18   8.66    8.9   9.02   9.14   9.39   4111    1.0\n",
      "mu[18]        9.04  2.8e-3   0.18   8.69   8.93   9.04   9.16    9.4   4096    1.0\n",
      "mu[19]        9.06  2.7e-3   0.17   8.72   8.95   9.06   9.18   9.41   4080    1.0\n",
      "mu[20]        9.08  2.6e-3   0.17   8.75   8.97   9.08   9.19   9.42   4062    1.0\n",
      "mu[21]         9.1  2.6e-3   0.16   8.78    9.0    9.1   9.21   9.43   4043    1.0\n",
      "mu[22]        9.12  2.5e-3   0.16   8.81   9.02   9.12   9.23   9.45   4023    1.0\n",
      "mu[23]        9.14  2.5e-3   0.16   8.83   9.04   9.14   9.25   9.46   4002    1.0\n",
      "mu[24]        9.16  2.4e-3   0.15   8.86   9.06   9.16   9.27   9.47   3980    1.0\n",
      "mu[25]        9.18  2.4e-3   0.15   8.88   9.09   9.18   9.28   9.49   3951    1.0\n",
      "mu[26]         9.2  2.4e-3   0.15   8.91   9.11    9.2    9.3    9.5   3918    1.0\n",
      "mu[27]        9.22  2.4e-3   0.15   8.93   9.13   9.22   9.32   9.52   3884    1.0\n",
      "mu[28]        9.24  2.4e-3   0.15   8.95   9.15   9.24   9.34   9.54   3849    1.0\n",
      "mu[29]        9.26  2.3e-3   0.14   8.97   9.17   9.26   9.36   9.55   3815    1.0\n",
      "mu[30]        9.28  2.3e-3   0.14    9.0   9.19   9.28   9.38   9.57   3781    1.0\n",
      "mu[31]         9.3  2.4e-3   0.14   9.02   9.21    9.3    9.4    9.6   3749    1.0\n",
      "mu[32]        9.32  2.4e-3   0.14   9.03   9.23   9.32   9.42   9.62   3718    1.0\n",
      "mu[33]        9.34  2.4e-3   0.14   9.05   9.25   9.35   9.44   9.64   3690    1.0\n",
      "mu[34]        9.36  2.4e-3   0.15   9.07   9.27   9.37   9.46   9.66   3665    1.0\n",
      "mu[35]        9.38  2.4e-3   0.15   9.09   9.28   9.39   9.48   9.68   3643    1.0\n",
      "mu[36]         9.4  2.5e-3   0.15    9.1    9.3    9.4    9.5    9.7   3623    1.0\n",
      "mu[37]        9.42  2.5e-3   0.15   9.12   9.32   9.43   9.52   9.73   3607    1.0\n",
      "mu[38]        9.44  2.6e-3   0.15   9.13   9.34   9.45   9.55   9.75   3593    1.0\n",
      "mu[39]        9.46  2.6e-3   0.16   9.15   9.35   9.47   9.57   9.78   3583    1.0\n",
      "mu[40]        9.48  2.7e-3   0.16   9.16   9.37   9.48   9.59   9.81   3575    1.0\n",
      "mu[41]         9.5  2.8e-3   0.16   9.18   9.39    9.5   9.62   9.83   3565    1.0\n",
      "mu[42]        9.52  2.8e-3   0.17   9.19   9.41   9.52   9.64   9.86   3558    1.0\n",
      "mu[43]        9.54  2.9e-3   0.17    9.2   9.42   9.54   9.66   9.89   3553    1.0\n",
      "mu[44]        9.56  3.0e-3   0.18   9.21   9.44   9.56   9.68   9.92   3550    1.0\n",
      "mu[45]        9.58  3.1e-3   0.18   9.22   9.46   9.58   9.71   9.95   3549    1.0\n",
      "mu[46]         9.6  3.1e-3   0.19   9.23   9.48    9.6   9.73   9.97   3550    1.0\n",
      "mu[47]        9.62  3.2e-3   0.19   9.24   9.49   9.62   9.75   10.0   3552    1.0\n",
      "mu[48]        9.64  3.3e-3    0.2   9.26   9.51   9.64   9.78  10.03   3555    1.0\n",
      "mu[49]        9.66  3.4e-3    0.2   9.27   9.53   9.66    9.8  10.06   3559    1.0\n",
      "mu[50]        9.68  3.5e-3   0.21   9.28   9.54   9.68   9.82  10.09   3563    1.0\n",
      "mu[51]         9.7  3.6e-3   0.21   9.28   9.56    9.7   9.85  10.12   3569    1.0\n",
      "mu[52]        9.72  3.7e-3   0.22   9.29   9.58   9.72   9.87  10.15   3575    1.0\n",
      "mu[53]        9.74  3.8e-3   0.23   9.29   9.59   9.74   9.89  10.19   3581    1.0\n",
      "mu[54]        9.76  3.9e-3   0.23    9.3   9.61   9.76   9.92  10.22   3587    1.0\n",
      "mu[55]        9.78  4.0e-3   0.24   9.31   9.62   9.78   9.94  10.25   3594    1.0\n",
      "mu[56]         9.8  4.1e-3   0.25   9.31   9.64    9.8   9.97  10.28   3601    1.0\n",
      "mu[57]        9.82  4.2e-3   0.25   9.32   9.65   9.82   9.99  10.32   3608    1.0\n",
      "mu[58]        9.84  4.3e-3   0.26   9.33   9.67   9.84  10.02  10.35   3615    1.0\n",
      "mu[59]        9.86  4.4e-3   0.26   9.34   9.69   9.86  10.04  10.38   3622    1.0\n",
      "mu[60]        9.88  4.5e-3   0.27   9.34    9.7   9.88  10.06  10.42   3628    1.0\n",
      "mu[61]         9.9  4.6e-3   0.28   9.35   9.72    9.9  10.09  10.45   3635    1.0\n",
      "mu[62]        9.92  4.7e-3   0.28   9.36   9.73   9.92  10.11  10.48   3642    1.0\n",
      "sigma         1.13  1.8e-3   0.11   0.95   1.06   1.12    1.2   1.37   3457    1.0\n",
      "ypred         10.0    0.02   1.35   7.37   9.12  10.01   10.9  12.67   4002    1.0\n",
      "log_lik[1]   -1.13  2.3e-3   0.13  -1.43  -1.21  -1.12  -1.04  -0.92   3270    1.0\n",
      "log_lik[2]   -2.96  8.4e-3   0.54  -4.15  -3.29  -2.93  -2.58  -2.04   4060    1.0\n",
      "log_lik[3]   -1.24  2.4e-3   0.15  -1.58  -1.33  -1.22  -1.13  -0.99   4039    1.0\n",
      "log_lik[4]   -1.24  2.5e-3   0.15   -1.6  -1.33  -1.22  -1.13  -0.99   3799    1.0\n",
      "log_lik[5]   -1.25  2.5e-3   0.15  -1.61  -1.34  -1.23  -1.14   -1.0   3822    1.0\n",
      "log_lik[6]   -1.55  3.3e-3   0.22  -2.06  -1.68  -1.52   -1.4  -1.19   4295    1.0\n",
      "log_lik[7]   -1.08  1.9e-3    0.1  -1.31  -1.15  -1.07  -1.01  -0.89   3055    1.0\n",
      "log_lik[8]   -1.09  1.8e-3    0.1  -1.29  -1.15  -1.08  -1.01  -0.89   3158    1.0\n",
      "log_lik[9]   -2.89  7.2e-3   0.46  -3.87  -3.17  -2.86  -2.56  -2.09   4009    1.0\n",
      "log_lik[10]  -1.65  3.2e-3   0.21  -2.13  -1.78  -1.63   -1.5  -1.28   4328    1.0\n",
      "log_lik[11]  -1.74  3.4e-3   0.22  -2.24  -1.87  -1.71  -1.58  -1.36   4429    1.0\n",
      "log_lik[12]  -1.06  1.8e-3    0.1  -1.26  -1.12  -1.06  -0.99  -0.88   3066    1.0\n",
      "log_lik[13]  -1.22  2.0e-3   0.12  -1.49  -1.29  -1.21  -1.14   -1.0   3736    1.0\n",
      "log_lik[14]   -2.3  4.5e-3    0.3  -2.97  -2.49  -2.27  -2.09  -1.78   4487    1.0\n",
      "log_lik[15]  -1.09  1.7e-3    0.1   -1.3  -1.16  -1.09  -1.02  -0.91   3332    1.0\n",
      "log_lik[16]  -1.07  1.7e-3    0.1  -1.27  -1.13  -1.06   -1.0  -0.89   3201    1.0\n",
      "log_lik[17]  -1.86  3.2e-3   0.21  -2.33  -1.99  -1.84  -1.71   -1.5   4433    1.0\n",
      "log_lik[18]   -1.9  3.3e-3   0.21  -2.37  -2.03  -1.88  -1.75  -1.52   4138    1.0\n",
      "log_lik[19]  -2.55  5.2e-3   0.32  -3.27  -2.75  -2.53  -2.32  -1.99   3959    1.0\n",
      "log_lik[20]  -1.06  1.7e-3    0.1  -1.26  -1.12  -1.06   -1.0  -0.88   3248    1.0\n",
      "log_lik[21]  -2.98  6.3e-3   0.39  -3.83  -3.22  -2.95  -2.71  -2.29   3891    1.0\n",
      "log_lik[22]  -1.36  1.8e-3   0.12  -1.61  -1.43  -1.35  -1.27  -1.15   4167    1.0\n",
      "log_lik[23]  -1.41  1.9e-3   0.12  -1.68  -1.49  -1.41  -1.33   -1.2   4228    1.0\n",
      "log_lik[24]  -4.11  9.2e-3   0.57  -5.37  -4.46  -4.06   -3.7  -3.11   3836    1.0\n",
      "log_lik[25]  -1.43  1.9e-3   0.12   -1.7  -1.51  -1.43  -1.35  -1.21   3968    1.0\n",
      "log_lik[26]  -1.31  1.7e-3   0.11  -1.53  -1.37   -1.3  -1.23  -1.11   3795    1.0\n",
      "log_lik[27]  -1.08  1.6e-3   0.09  -1.27  -1.14  -1.08  -1.01   -0.9   3331    1.0\n",
      "log_lik[28]  -1.22  1.6e-3    0.1  -1.42  -1.28  -1.22  -1.15  -1.04   3637    1.0\n",
      "log_lik[29]  -1.76  2.5e-3   0.16  -2.11  -1.86  -1.75  -1.65  -1.48   4004    1.0\n",
      "log_lik[30]  -2.18  3.6e-3   0.22  -2.67  -2.33  -2.16  -2.02  -1.79   3914    1.0\n",
      "log_lik[31]  -2.08  3.3e-3   0.21  -2.53  -2.21  -2.06  -1.93  -1.72   3897    1.0\n",
      "log_lik[32]  -1.65  2.2e-3   0.14  -1.94  -1.73  -1.64  -1.55  -1.39   3921    1.0\n",
      "log_lik[33]   -1.4  1.8e-3   0.11  -1.64  -1.47   -1.4  -1.33   -1.2   3814    1.0\n",
      "log_lik[34]  -1.09  1.6e-3   0.09  -1.29  -1.15  -1.09  -1.03  -0.92   3324    1.0\n",
      "log_lik[35]  -1.05  1.6e-3   0.09  -1.25  -1.11  -1.05  -0.99  -0.88   3292    1.0\n",
      "log_lik[36]  -2.82  5.6e-3   0.34  -3.55  -3.04  -2.79  -2.58  -2.23   3671    1.0\n",
      "log_lik[37]  -1.36  1.9e-3   0.11  -1.59  -1.43  -1.35  -1.28  -1.16   3608    1.0\n",
      "log_lik[38]  -1.06  1.6e-3   0.09  -1.25  -1.12  -1.05  -0.99  -0.88   3274    1.0\n",
      "log_lik[39]  -1.33  1.9e-3   0.11  -1.57   -1.4  -1.32  -1.25  -1.13   3549    1.0\n",
      "log_lik[40]  -1.09  1.7e-3    0.1  -1.29  -1.15  -1.09  -1.02  -0.91   3273    1.0\n",
      "log_lik[41]  -1.15  1.7e-3    0.1  -1.36  -1.21  -1.15  -1.08  -0.97   3270    1.0\n",
      "log_lik[42]  -1.12  1.7e-3    0.1  -1.33  -1.18  -1.12  -1.05  -0.94   3231    1.0\n",
      "log_lik[43]  -1.05  1.7e-3   0.09  -1.24  -1.11  -1.05  -0.99  -0.87   3248    1.0\n",
      "log_lik[44]  -1.35  2.1e-3   0.13  -1.63  -1.43  -1.34  -1.26  -1.13   3578    1.0\n",
      "log_lik[45]  -1.09  1.7e-3    0.1   -1.3  -1.16  -1.09  -1.02  -0.91   3226    1.0\n",
      "log_lik[46]  -1.37  2.3e-3   0.14  -1.67  -1.46  -1.37  -1.27  -1.13   3569    1.0\n",
      "log_lik[47]  -1.07  1.7e-3    0.1  -1.27  -1.13  -1.07  -1.01  -0.89   3118    1.0\n",
      "log_lik[48]  -1.22  2.0e-3   0.12  -1.48  -1.29  -1.21  -1.14  -1.01   3404    1.0\n",
      "log_lik[49]  -1.23  2.1e-3   0.12   -1.5  -1.31  -1.22  -1.14  -1.02   3432    1.0\n",
      "log_lik[50]  -1.06  1.7e-3    0.1  -1.25  -1.12  -1.05  -0.99  -0.87   3119    1.0\n",
      "log_lik[51]  -2.21  4.9e-3   0.31  -2.86   -2.4  -2.18  -1.99  -1.68   3862    1.0\n",
      "log_lik[52]  -1.44  2.9e-3   0.17  -1.82  -1.54  -1.42  -1.31  -1.14   3650    1.0\n",
      "log_lik[53]  -1.11  1.9e-3   0.11  -1.34  -1.18   -1.1  -1.03  -0.91   3167    1.0\n",
      "log_lik[54]  -1.49  3.2e-3   0.19  -1.91  -1.61  -1.47  -1.35  -1.16   3698    1.0\n",
      "log_lik[55]  -1.21  2.4e-3   0.14  -1.52   -1.3   -1.2  -1.11  -0.98   3387    1.0\n",
      "log_lik[56]  -1.16  2.2e-3   0.13  -1.44  -1.24  -1.15  -1.07  -0.94   3272    1.0\n",
      "log_lik[57]  -1.48  3.4e-3   0.21  -1.95  -1.61  -1.46  -1.33  -1.15   3732    1.0\n",
      "log_lik[58]  -1.06  1.9e-3    0.1  -1.28  -1.13  -1.06   -1.0  -0.88   2819    1.0\n",
      "log_lik[59]  -1.52  3.7e-3   0.22  -2.03  -1.65  -1.49  -1.35  -1.16   3760    1.0\n",
      "log_lik[60]   -1.4  3.3e-3    0.2  -1.87  -1.52  -1.38  -1.26  -1.07   3660    1.0\n",
      "log_lik[61]  -1.75  4.7e-3   0.29  -2.42  -1.93  -1.71  -1.54  -1.28   3799    1.0\n",
      "log_lik[62]  -1.62  4.3e-3   0.27  -2.23  -1.79   -1.6  -1.43  -1.19   3814    1.0\n",
      "lp__         -28.8    0.03   1.24 -31.96  -29.4 -28.48 -27.88 -27.39   1878    1.0\n",
      "\n",
      "Samples were drawn using NUTS at Wed Dec 19 11:19:44 2018.\n",
      "For each parameter, n_eff is a crude measure of effective sample size,\n",
      "and Rhat is the potential scale reduction factor on split chains (at \n",
      "convergence, Rhat=1).\n"
     ]
    }
   ],
   "source": [
    "print(fit_lin_std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get now much better effective sample sizes `n_eff`.\n",
    "\n",
    "Check the treedepth, E-BFMI, and divergences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 of 4000 iterations saturated the maximum tree depth of 10 (0.0%)\n",
      "0.0 of 4000 iterations ended with a divergence (0.0%)\n"
     ]
    }
   ],
   "source": [
    "stan_utility.check_treedepth(fit_lin_std)\n",
    "stan_utility.check_energy(fit_lin_std)\n",
    "stan_utility.check_div(fit_lin_std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Everything is fine now. The next figure shows that with the standardized data there is not much posterior correlation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x388.8 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples = fit_lin_std.extract(permuted=True)\n",
    "plt.figure()\n",
    "# preview 2000 samples\n",
    "plt.scatter(samples['alpha'][:2000], samples['beta'][:2000], 50, marker='.', alpha=0.25)\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('beta');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the probability that the summer temperature is increasing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pr(beta > 0) = 0.991\n"
     ]
    }
   ],
   "source": [
    "print('Pr(beta > 0) = {}'.format(np.mean(samples['beta'] > 0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the data, the model fit and prediction for year 2016."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1108.8x466.56 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1382.4x345.6 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# make slightly wider figure of 3 plots\n",
    "figsize = plt.rcParams['figure.figsize'].copy()\n",
    "figsize[0] *= 2.2  # width\n",
    "figsize[1] *= 1.2  # width\n",
    "fig, ax = plt.subplots(1, 1, figsize=figsize)\n",
    "\n",
    "# plot 1: scatterplot and lines\n",
    "color_scatter = 'C0'  # 'C0' for default color #0\n",
    "color_line = 'C3'     # 'C1' for default color #1\n",
    "\n",
    "ax.fill_between(\n",
    "    x,\n",
    "    np.percentile(samples['mu'], 5, axis=0),\n",
    "    np.percentile(samples['mu'], 95, axis=0),\n",
    "    # lighten color_line\n",
    "    color=1 - 0.4*(1 - np.array(mpl.colors.to_rgb(color_line)))\n",
    ")\n",
    "ax.plot(\n",
    "    x,\n",
    "    np.percentile(samples['mu'], 50, axis=0),\n",
    "    color=color_line,\n",
    "    linewidth=2,\n",
    "    alpha=0.8\n",
    ")\n",
    "ax.scatter(x, y, 10, color=color_scatter)\n",
    "ax.set_xlabel('year')\n",
    "ax.set_ylabel('summer temp. @Kilpisjarvi')\n",
    "ax.set_xlim((1951.5, 2013.5))\n",
    "\n",
    "az.plot_posterior(fit_lin_std, var_names=['beta','sigma','ypred'], credible_interval=0.95, round_to=2, kind='hist', bins=35)\n",
    "plt.xlabel('y-prediction for x={}'.format(xpred));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can also plot ridgeplot for mu samples. Ridge plot better illustrates the fact that each year is represented by distribution for mu parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 648x504 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Make complementary ridge plot\n",
    "fig, axes = az.plot_forest(fit_lin_std,\n",
    "                           kind='ridgeplot',\n",
    "                           var_names=['mu'],\n",
    "                           combined=True,\n",
    "                           r_hat = False,\n",
    "                           n_eff = True,\n",
    "                           ridgeplot_overlap=5,\n",
    "                           ridgeplot_alpha=0.7,\n",
    "                           colors='lightblue',\n",
    "                           figsize=(9, 7))\n",
    "# Let's adjust labels (default arviz labels are not so good for large amount of distributions)\n",
    "axes[0].set_yticklabels(\n",
    "    [str(year) if year % 2 == 0 else '' for year in range(2013, 1952-1, -1)])\n",
    "axes[0].set_ylabel('Year')\n",
    "axes[0].set_xlabel('Average temperature')\n",
    "# make figure compact\n",
    "fig.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Student's t model.\n",
    "\n",
    "The temperatures used in the above analyses are averages over three months, which makes it more likely that they are normally distributed, but there can be extreme events in the weather and we can check whether more robust Student's t observation model would give different results. For the Student's t distribution we also need the degree of freedom, nu, as an additional parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "// Linear student-t model\n",
      "data {\n",
      "  int<lower=0> N; // number of data points\n",
      "  vector[N] x; //\n",
      "  vector[N] y; //\n",
      "  real xpred; // input location for prediction\n",
      "}\n",
      "parameters {\n",
      "  real alpha;\n",
      "  real beta;\n",
      "  real<lower=0> sigma;\n",
      "  real<lower=1, upper=80> nu;\n",
      "}\n",
      "transformed parameters {\n",
      "  vector[N] mu;\n",
      "  mu = alpha + beta*x;\n",
      "}\n",
      "model {\n",
      "  nu ~ gamma(2, 0.1); // Juarez and Steel(2010)\n",
      "  y ~ student_t(nu, mu, sigma);\n",
      "}\n",
      "generated quantities {\n",
      "  real ypred;\n",
      "  vector[N] log_lik;\n",
      "  ypred = normal_rng(alpha + beta*xpred, sigma);\n",
      "  for (i in 1:N)\n",
      "    log_lik[i] = student_t_lpdf(y[i] | nu, mu[i], sigma);\n",
      "}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with open('lin_t.stan') as file:\n",
    "    print(file.read())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:pystan:108 of 4000 iterations saturated the maximum tree depth of 10 (2.7%)\n",
      "WARNING:pystan:Run again with max_treedepth larger than 10 to avoid saturation\n"
     ]
    }
   ],
   "source": [
    "model = stan_utility.compile_model('lin_t.stan')\n",
    "fit_lin_t = model.sampling(data=data, seed=194838)\n",
    "samples = fit.extract(permuted=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the `n_eff` and `Rhat`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inference for Stan model: anon_model_985e43a8fe28088e3317d00edd324bab.\n",
      "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
      "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
      "\n",
      "              mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
      "alpha       -32.55    0.44  16.05 -64.15 -43.72 -32.53  -21.6  -0.96   1343    1.0\n",
      "beta          0.02  2.2e-4 8.1e-3 5.2e-3   0.02   0.02   0.03   0.04   1342    1.0\n",
      "sigma         1.08  2.6e-3   0.11   0.88    1.0   1.08   1.15   1.32   1827    1.0\n",
      "nu           23.97    0.33  13.37   5.72  14.18   21.2  30.96  57.83   1670    1.0\n",
      "mu[1]         8.67  7.1e-3   0.29   8.11   8.47   8.66   8.87   9.24   1684    1.0\n",
      "mu[2]         8.69  6.9e-3   0.28   8.14    8.5   8.69   8.89   9.25   1701    1.0\n",
      "mu[3]         8.71  6.6e-3   0.28   8.18   8.53   8.71    8.9   9.25   1721    1.0\n",
      "mu[4]         8.73  6.4e-3   0.27   8.21   8.55   8.73   8.92   9.26   1742    1.0\n",
      "mu[5]         8.75  6.2e-3   0.26   8.25   8.58   8.75   8.94   9.26   1765    1.0\n",
      "mu[6]         8.78  6.0e-3   0.26   8.28    8.6   8.77   8.95   9.27   1790    1.0\n",
      "mu[7]          8.8  5.8e-3   0.25   8.31   8.63    8.8   8.97   9.28   1817    1.0\n",
      "mu[8]         8.82  5.6e-3   0.24   8.35   8.65   8.82   8.99   9.28   1848    1.0\n",
      "mu[9]         8.84  5.4e-3   0.24   8.38   8.68   8.84    9.0   9.29   1881    1.0\n",
      "mu[10]        8.86  5.2e-3   0.23   8.41    8.7   8.86   9.02    9.3   1918    1.0\n",
      "mu[11]        8.88  5.0e-3   0.22   8.44   8.73   8.88   9.04   9.31   1959    1.0\n",
      "mu[12]         8.9  4.8e-3   0.22   8.48   8.75    8.9   9.05   9.32   2004    1.0\n",
      "mu[13]        8.92  4.7e-3   0.21   8.51   8.78   8.92   9.07   9.33   2054    1.0\n",
      "mu[14]        8.94  4.5e-3   0.21   8.54    8.8   8.94   9.09   9.34   2110    1.0\n",
      "mu[15]        8.97  4.3e-3    0.2   8.57   8.83   8.97    9.1   9.35   2172    1.0\n",
      "mu[16]        8.99  4.1e-3   0.19    8.6   8.86   8.99   9.12   9.36   2241    1.0\n",
      "mu[17]        9.01  3.9e-3   0.19   8.63   8.88   9.01   9.14   9.37   2317    1.0\n",
      "mu[18]        9.03  3.7e-3   0.18   8.66   8.91   9.03   9.15   9.38   2401    1.0\n",
      "mu[19]        9.05  3.6e-3   0.18   8.69   8.93   9.05   9.17    9.4   2496    1.0\n",
      "mu[20]        9.07  3.4e-3   0.17   8.72   8.96   9.07   9.19   9.41   2600    1.0\n",
      "mu[21]        9.09  3.3e-3   0.17   8.75   8.98   9.09   9.21   9.42   2715    1.0\n",
      "mu[22]        9.11  3.1e-3   0.17   8.78   9.01   9.12   9.23   9.43   2841    1.0\n",
      "mu[23]        9.14  3.0e-3   0.16   8.81   9.03   9.14   9.24   9.45   2978    1.0\n",
      "mu[24]        9.16  2.8e-3   0.16   8.83   9.05   9.16   9.26   9.46   3123    1.0\n",
      "mu[25]        9.18  2.7e-3   0.16   8.86   9.07   9.18   9.28   9.48   3274    1.0\n",
      "mu[26]         9.2  2.6e-3   0.15   8.89    9.1    9.2    9.3    9.5   3427    1.0\n",
      "mu[27]        9.22  2.5e-3   0.15   8.92   9.12   9.22   9.32   9.52   3613    1.0\n",
      "mu[28]        9.24  2.4e-3   0.15   8.94   9.14   9.24   9.34   9.53   3814    1.0\n",
      "mu[29]        9.26  2.3e-3   0.15   8.97   9.16   9.26   9.36   9.55   3991    1.0\n",
      "mu[30]        9.28  2.3e-3   0.15   8.99   9.19   9.29   9.38   9.57   4125    1.0\n",
      "mu[31]         9.3  2.2e-3   0.14   9.02   9.21   9.31    9.4   9.59   4201    1.0\n",
      "mu[32]        9.33  2.2e-3   0.14   9.04   9.23   9.33   9.42   9.61   4209    1.0\n",
      "mu[33]        9.35  2.2e-3   0.14   9.06   9.25   9.35   9.44   9.63   4146    1.0\n",
      "mu[34]        9.37  2.3e-3   0.15   9.08   9.27   9.37   9.46   9.66   4022    1.0\n",
      "mu[35]        9.39  2.4e-3   0.15    9.1   9.29   9.39   9.49   9.68   3850    1.0\n",
      "mu[36]        9.41  2.5e-3   0.15   9.12   9.31   9.41   9.51   9.71   3648    1.0\n",
      "mu[37]        9.43  2.6e-3   0.15   9.14   9.33   9.43   9.53   9.73   3432    1.0\n",
      "mu[38]        9.45  2.7e-3   0.15   9.16   9.35   9.45   9.55   9.76   3216    1.0\n",
      "mu[39]        9.47  2.8e-3   0.16   9.17   9.37   9.48   9.57   9.79   3054    1.0\n",
      "mu[40]        9.49  2.9e-3   0.16   9.19   9.39   9.49    9.6   9.81   2903    1.0\n",
      "mu[41]        9.52  3.1e-3   0.16   9.21    9.4   9.51   9.62   9.84   2763    1.0\n",
      "mu[42]        9.54  3.2e-3   0.17   9.22   9.42   9.54   9.64   9.87   2634    1.0\n",
      "mu[43]        9.56  3.4e-3   0.17   9.24   9.44   9.56   9.67    9.9   2517    1.0\n",
      "mu[44]        9.58  3.6e-3   0.17   9.25   9.46   9.58   9.69   9.93   2404    1.0\n",
      "mu[45]         9.6  3.7e-3   0.18   9.26   9.48    9.6   9.72   9.96   2302    1.0\n",
      "mu[46]        9.62  3.9e-3   0.18   9.27    9.5   9.62   9.74   9.99   2212    1.0\n",
      "mu[47]        9.64  4.1e-3   0.19   9.28   9.51   9.64   9.76  10.02   2132    1.0\n",
      "mu[48]        9.66  4.3e-3   0.19    9.3   9.53   9.66   9.79  10.05   2062    1.0\n",
      "mu[49]        9.68  4.5e-3    0.2    9.3   9.55   9.68   9.81  10.08   1999    1.0\n",
      "mu[50]        9.71  4.7e-3   0.21   9.32   9.56    9.7   9.84  10.12   1943    1.0\n",
      "mu[51]        9.73  4.9e-3   0.21   9.33   9.58   9.72   9.87  10.15   1893    1.0\n",
      "mu[52]        9.75  5.0e-3   0.22   9.34    9.6   9.74   9.89  10.18   1848    1.0\n",
      "mu[53]        9.77  5.2e-3   0.22   9.34   9.61   9.76   9.92  10.22   1808    1.0\n",
      "mu[54]        9.79  5.4e-3   0.23   9.35   9.63   9.79   9.94  10.25   1772    1.0\n",
      "mu[55]        9.81  5.6e-3   0.24   9.36   9.65   9.81   9.97  10.29   1740    1.0\n",
      "mu[56]        9.83  5.9e-3   0.24   9.37   9.67   9.83   9.99  10.32   1711    1.0\n",
      "mu[57]        9.85  6.1e-3   0.25   9.38   9.68   9.85  10.02  10.35   1685    1.0\n",
      "mu[58]        9.87  6.3e-3   0.26   9.38    9.7   9.87  10.04  10.39   1661    1.0\n",
      "mu[59]         9.9  6.5e-3   0.26   9.39   9.72   9.89  10.07  10.42   1640    1.0\n",
      "mu[60]        9.92  6.7e-3   0.27    9.4   9.73   9.91   10.1  10.45   1620    1.0\n",
      "mu[61]        9.94  6.9e-3   0.28    9.4   9.75   9.93  10.12  10.49   1602    1.0\n",
      "mu[62]        9.96  7.1e-3   0.28   9.41   9.77   9.95  10.15  10.52   1586    1.0\n",
      "ypred         10.0    0.02   1.11   7.81   9.25  10.01  10.77  12.16   3687    1.0\n",
      "log_lik[1]   -1.11  3.4e-3   0.14  -1.43  -1.19   -1.1  -1.01  -0.87   1758    1.0\n",
      "log_lik[2]   -3.05    0.01   0.53  -4.17  -3.39   -3.0  -2.66  -2.12   1816    1.0\n",
      "log_lik[3]   -1.26  4.2e-3   0.18  -1.67  -1.36  -1.23  -1.13  -0.97   1868    1.0\n",
      "log_lik[4]   -1.22  4.1e-3   0.17  -1.61  -1.33  -1.21   -1.1  -0.94   1772    1.0\n",
      "log_lik[5]   -1.23  4.0e-3   0.17  -1.62  -1.34  -1.22  -1.11  -0.95   1792    1.0\n",
      "log_lik[6]   -1.55  5.6e-3   0.24  -2.09   -1.7  -1.53  -1.38  -1.16   1829    1.0\n",
      "log_lik[7]   -1.05  2.6e-3   0.11  -1.29  -1.12  -1.05  -0.98  -0.84   1873    1.0\n",
      "log_lik[8]   -1.07  2.5e-3   0.12  -1.32  -1.14  -1.06  -0.99  -0.87   2040    1.0\n",
      "log_lik[9]   -2.96    0.01   0.45  -3.94  -3.26  -2.92  -2.64  -2.18   1949    1.0\n",
      "log_lik[10]  -1.71  5.6e-3   0.25  -2.25  -1.87  -1.69  -1.53   -1.3   1950    1.0\n",
      "log_lik[11]  -1.76  5.5e-3   0.24  -2.29  -1.91  -1.73  -1.58  -1.34   1999    1.0\n",
      "log_lik[12]  -1.03  2.4e-3    0.1  -1.25   -1.1  -1.03  -0.96  -0.83   1887    1.0\n",
      "log_lik[13]  -1.21  3.1e-3   0.14   -1.5  -1.29   -1.2  -1.11  -0.96   2003    1.0\n",
      "log_lik[14]  -2.33  6.8e-3   0.31  -2.99  -2.53  -2.31  -2.11  -1.78   2135    1.0\n",
      "log_lik[15]  -1.08  2.4e-3   0.11  -1.31  -1.15  -1.07   -1.0  -0.88   2057    1.0\n",
      "log_lik[16]  -1.04  2.4e-3    0.1  -1.26  -1.11  -1.04  -0.97  -0.84   1910    1.0\n",
      "log_lik[17]   -1.9  4.8e-3   0.23  -2.39  -2.04  -1.88  -1.73   -1.5   2305    1.0\n",
      "log_lik[18]  -1.97  5.1e-3   0.24  -2.51  -2.12  -1.95   -1.8  -1.57   2284    1.0\n",
      "log_lik[19]  -2.63  7.0e-3   0.33  -3.36  -2.84  -2.59  -2.38  -2.06   2273    1.0\n",
      "log_lik[20]  -1.03  2.4e-3    0.1  -1.24   -1.1  -1.03  -0.97  -0.84   1901    1.0\n",
      "log_lik[21]  -3.03  7.9e-3   0.38  -3.85  -3.27   -3.0  -2.76  -2.38   2335    1.0\n",
      "log_lik[22]  -1.38  2.5e-3   0.14  -1.67  -1.46  -1.37  -1.28  -1.14   2858    1.0\n",
      "log_lik[23]  -1.44  2.6e-3   0.14  -1.74  -1.53  -1.43  -1.34  -1.19   2976    1.0\n",
      "log_lik[24]  -3.99  9.6e-3   0.49  -5.04  -4.31  -3.96  -3.65  -3.11   2636    1.0\n",
      "log_lik[25]  -1.45  2.5e-3   0.14  -1.74  -1.54  -1.44  -1.36  -1.21   3061    1.0\n",
      "log_lik[26]  -1.31  2.2e-3   0.12  -1.55  -1.39  -1.31  -1.23  -1.09   2938    1.0\n",
      "log_lik[27]  -1.05  2.3e-3    0.1  -1.25  -1.12  -1.05  -0.98  -0.87   1943    1.0\n",
      "log_lik[28]  -1.22  1.9e-3   0.11  -1.44  -1.28  -1.21  -1.15  -1.02   3121    1.0\n",
      "log_lik[29]  -1.81  3.1e-3   0.18   -2.2  -1.92   -1.8  -1.69   -1.5   3309    1.0\n",
      "log_lik[30]  -2.24  4.2e-3   0.23  -2.73  -2.39  -2.23  -2.08  -1.82   3003    1.0\n",
      "log_lik[31]  -2.14  3.9e-3   0.22  -2.59  -2.27  -2.12  -1.98  -1.75   3119    1.0\n",
      "log_lik[32]  -1.69  2.5e-3   0.16  -2.02  -1.78  -1.68  -1.58  -1.41   3715    1.0\n",
      "log_lik[33]  -1.42  2.1e-3   0.12  -1.68   -1.5  -1.42  -1.34   -1.2   3615    1.0\n",
      "log_lik[34]  -1.07  2.2e-3    0.1  -1.27  -1.13  -1.07   -1.0  -0.88   2068    1.0\n",
      "log_lik[35]  -1.02  2.4e-3    0.1  -1.23  -1.09  -1.02  -0.96  -0.83   1801    1.0\n",
      "log_lik[36]  -2.87  6.3e-3   0.32  -3.55  -3.08  -2.85  -2.64   -2.3   2660    1.0\n",
      "log_lik[37]  -1.36  2.0e-3   0.12  -1.61  -1.44  -1.35  -1.28  -1.14   3533    1.0\n",
      "log_lik[38]  -1.03  2.3e-3    0.1  -1.23  -1.09  -1.03  -0.96  -0.83   1835    1.0\n",
      "log_lik[39]  -1.33  2.1e-3   0.12  -1.58  -1.41  -1.32  -1.25  -1.11   3182    1.0\n",
      "log_lik[40]  -1.06  2.2e-3    0.1  -1.26  -1.13  -1.06  -0.99  -0.87   2039    1.0\n",
      "log_lik[41]  -1.14  2.3e-3   0.11  -1.37  -1.21  -1.14  -1.07  -0.94   2191    1.0\n",
      "log_lik[42]  -1.11  2.4e-3   0.11  -1.33  -1.18   -1.1  -1.03  -0.91   2083    1.0\n",
      "log_lik[43]  -1.02  2.4e-3    0.1  -1.23  -1.09  -1.02  -0.95  -0.82   1794    1.0\n",
      "log_lik[44]  -1.37  2.9e-3   0.14  -1.67  -1.46  -1.36  -1.27  -1.13   2302    1.0\n",
      "log_lik[45]  -1.06  2.3e-3    0.1  -1.27  -1.13  -1.06  -0.99  -0.86   2004    1.0\n",
      "log_lik[46]  -1.37  3.0e-3   0.15  -1.68  -1.47  -1.37  -1.27  -1.12   2401    1.0\n",
      "log_lik[47]  -1.05  2.4e-3   0.11  -1.27  -1.12  -1.05  -0.98  -0.85   1900    1.0\n",
      "log_lik[48]  -1.23  2.9e-3   0.13  -1.51  -1.31  -1.22  -1.13  -0.99   2071    1.0\n",
      "log_lik[49]  -1.24  3.1e-3   0.14  -1.54  -1.32  -1.23  -1.14   -1.0   2039    1.0\n",
      "log_lik[50]  -1.03  2.4e-3    0.1  -1.24  -1.09  -1.02  -0.96  -0.83   1844    1.0\n",
      "log_lik[51]  -2.24  6.9e-3   0.31  -2.88  -2.43  -2.22  -2.02  -1.69   1997    1.0\n",
      "log_lik[52]  -1.44  4.1e-3   0.18  -1.83  -1.55  -1.42  -1.31  -1.13   1966    1.0\n",
      "log_lik[53]  -1.08  2.6e-3   0.11  -1.32  -1.15  -1.08   -1.0  -0.87   1916    1.0\n",
      "log_lik[54]  -1.49  4.6e-3    0.2  -1.93  -1.62  -1.47  -1.35  -1.15   1887    1.0\n",
      "log_lik[55]  -1.19  3.3e-3   0.14   -1.5  -1.28  -1.18  -1.09  -0.94   1880    1.0\n",
      "log_lik[56]  -1.13  3.1e-3   0.13  -1.42  -1.22  -1.12  -1.04   -0.9   1857    1.0\n",
      "log_lik[57]  -1.53  5.5e-3   0.23  -2.05  -1.68  -1.51  -1.37  -1.16   1745    1.0\n",
      "log_lik[58]  -1.04  2.5e-3   0.11  -1.27  -1.11  -1.04  -0.97  -0.83   1937    1.0\n",
      "log_lik[59]  -1.57  6.1e-3   0.25  -2.14  -1.73  -1.54  -1.39  -1.17   1704    1.0\n",
      "log_lik[60]  -1.39  5.1e-3   0.21  -1.88  -1.52  -1.37  -1.24  -1.05   1707    1.0\n",
      "log_lik[61]  -1.83  7.7e-3   0.32  -2.53  -2.02   -1.8   -1.6  -1.31   1656    1.0\n",
      "log_lik[62]  -1.62  6.7e-3   0.28  -2.25  -1.79   -1.6  -1.42  -1.17   1680    1.0\n",
      "lp__        -56.54    0.04   1.47 -60.15  -57.3 -56.18 -55.45 -54.71   1362    1.0\n",
      "\n",
      "Samples were drawn using NUTS at Wed Dec 19 11:20:12 2018.\n",
      "For each parameter, n_eff is a crude measure of effective sample size,\n",
      "and Rhat is the potential scale reduction factor on split chains (at \n",
      "convergence, Rhat=1).\n"
     ]
    }
   ],
   "source": [
    "print(fit_lin_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again without standardization we get smaller n_eff's, but large enough for practical purposes.\n",
    "\n",
    "Check the treedepth, E-BFMI, and divergences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "108 of 4000 iterations saturated the maximum tree depth of 10 (2.7%)\n",
      "Run again with max_depth set to a larger value to avoid saturation\n",
      "0.0 of 4000 iterations ended with a divergence (0.0%)\n"
     ]
    }
   ],
   "source": [
    "stan_utility.check_treedepth(fit_lin_t)\n",
    "stan_utility.check_energy(fit_lin_t)\n",
    "stan_utility.check_div(fit_lin_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see again many iterations saturating the maximum tree depth, which is harmful for the efficiency but doesn't invalidate the results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the probability that the summer temperature is increasing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pr(beta > 0) = 0.9965\n"
     ]
    }
   ],
   "source": [
    "samples = fit_lin_t.extract(permuted=True)\n",
    "print('Pr(beta > 0) = {}'.format(np.mean(samples['beta'] > 0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get similar probability as with Gaussian obervation model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the data, the model fit, and the marginal posteriors for sigma and nu."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1108.8x466.56 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 921.6x345.6 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 921.6x345.6 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figsize = plt.rcParams['figure.figsize'].copy()\n",
    "figsize[0] *= 2.2  # width\n",
    "figsize[1] *= 1.2  # width\n",
    "fig, ax = plt.subplots(1, 1, figsize=figsize)\n",
    "\n",
    "# plot 1: scatterplot and lines\n",
    "color_scatter = 'C0'  # 'C0' for default color #0\n",
    "color_line = 'C3'     # 'C1' for default color #1\n",
    "\n",
    "ax.fill_between(\n",
    "    x,\n",
    "    np.percentile(samples['mu'], 5, axis=0),\n",
    "    np.percentile(samples['mu'], 95, axis=0),\n",
    "    # lighten color_line\n",
    "    color=1 - 0.4*(1 - np.array(mpl.colors.to_rgb(color_line)))\n",
    ")\n",
    "ax.plot(\n",
    "    x,\n",
    "    np.percentile(samples['mu'], 50, axis=0),\n",
    "    color=color_line,\n",
    "    linewidth=2,\n",
    "    alpha=0.8\n",
    ")\n",
    "ax.scatter(x, y, 10, color=color_scatter)\n",
    "ax.set_xlabel('year')\n",
    "ax.set_ylabel('summer temp. @Kilpisjarvi')\n",
    "ax.set_xlim((1951.5, 2013.5))\n",
    "\n",
    "az.plot_posterior(fit_lin_t, var_names=['beta','sigma'], credible_interval=0.95, round_to=2, kind='hist', bins=35)\n",
    "az.plot_posterior(fit_lin_t, var_names=['ypred', 'nu'], credible_interval=0.95, round_to=2, kind='hist', bins=35)\n",
    "\n",
    "plt.xlabel('y-prediction for x={}'.format(xpred));\n",
    "# make figure compact\n",
    "fig.tight_layout();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior of the degree of freedom \"nu\" reveals that Gaussian model is likely to be ok, as Student's t with `nu > 20` is very close to Gaussian."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pareto-smoothed importance-sampling leave-one-out cross-validation (PSIS-LOO)\n",
    "We can use leave-one-out cross-validation to compare the expected predictive performance. For the following three lines to execute, the log-likelihood needs to be evaluated in the stan code. For an example, see:\n",
    "- stan file lin.stan \n",
    "- [ArviZ API](https://arviz-devs.github.io/arviz/api.html) (for Python) \n",
    "- [Computing approximate leave-one-out cross-validation usig PSIS-LOO](http://mc-stan.org/loo/articles/loo2-with-rstan.html) (In R). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                    loo     ploo      dloo weight       se       dse warning\n",
      "linear_model    192.957  2.80436         0      1  10.0009         0       0\n",
      "linear_model_t  193.434   2.7311  0.477703      0  10.1958  0.847232       0\n"
     ]
    }
   ],
   "source": [
    "# Convert stan objects to ArviZ inference data objects\n",
    "inference_lin = az.convert_to_inference_data(fit_lin, log_likelihood='log_lik')\n",
    "inference_lin_t = az.convert_to_inference_data(fit_lin_t, log_likelihood='log_lik')\n",
    "\n",
    "# Store inference data objects to dictionary\n",
    "models = dict([\n",
    "         (\"linear_model\", inference_lin),\n",
    "         (\"linear_model_t\", inference_lin_t)\n",
    "             ])\n",
    "\n",
    "# Compare models with loo\n",
    "comparison = az.compare(models, ic='loo')\n",
    "print(comparison)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Loo values are similar for models. Hence, there is no practical difference between Gaussian and Student’s t observation model for this data.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Comparison of k groups with hierarchical models\n",
    "\n",
    "In following, for each year, we analyze the monthly average temperatures for three summer months: June, July and August. In previous example, we used the average of these three summer months as estimate for yearly average summer temperarute. Now we would like to know, if there is a difference between three summer months: June, July and August."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "data_path = os.path.abspath(\n",
    "    os.path.join(\n",
    "        os.path.pardir,\n",
    "        'utilities_and_data',\n",
    "        'kilpisjarvi-summer-temp.csv'\n",
    "    )\n",
    ")\n",
    "# Load data\n",
    "d = np.loadtxt(data_path, dtype=np.double, delimiter=';', skiprows=1)\n",
    "# summer months are numbered from 1 to 3\n",
    "x = np.tile(np.arange(1, 4), d.shape[0]) # create array with repeating numbers 1,2,3 for each year\n",
    "y = d[:, 1:4].ravel()\n",
    "N = len(x)\n",
    "data = dict(\n",
    "    N = N,\n",
    "    K = 3,  # 3 groups\n",
    "    x = x,  # group indicators\n",
    "    y = y)  # observations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Common variance (ANOVA) model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "// Comparison of k groups with common variance (ANOVA)\n",
      "data {\n",
      "  int<lower=0> N; // number of data points\n",
      "  int<lower=0> K; // number of groups\n",
      "  int<lower=1,upper=K> x[N]; // group indicator\n",
      "  vector[N] y; //\n",
      "}\n",
      "parameters {\n",
      "  vector[K] mu;        // group means\n",
      "  real<lower=0> sigma; // common std\n",
      "}\n",
      "model {\n",
      "  y ~ normal(mu[x], sigma);\n",
      "}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with open('grp_aov.stan') as file:\n",
    "    print(file.read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    }
   ],
   "source": [
    "model = stan_utility.compile_model('grp_aov.stan')\n",
    "fit = model.sampling(data=data, seed=194838)\n",
    "samples = fit.extract(permuted=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the `n_eff` and `Rhat` values for sampled model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Inference for Stan model: anon_model_7564a28d1f0313ff396284979a4361d6.\n",
      "4 chains, each with iter=2000; warmup=1000; thin=1; \n",
      "post-warmup draws per chain=1000, total post-warmup draws=4000.\n",
      "\n",
      "        mean se_mean     sd   2.5%    25%    50%    75%  97.5%  n_eff   Rhat\n",
      "mu[1]   7.54  2.9e-3    0.2   7.15   7.41   7.54   7.67   7.92   4644    1.0\n",
      "mu[2]  10.97  2.9e-3    0.2  10.58  10.83  10.97   11.1  11.35   4738    1.0\n",
      "mu[3]   9.44  2.7e-3   0.19   9.06    9.3   9.43   9.57   9.82   4937    1.0\n",
      "sigma   1.53  1.2e-3   0.08   1.38   1.47   1.53   1.58    1.7   4344    1.0\n",
      "lp__  -170.9    0.03    1.4 -174.3 -171.6 -170.5 -169.8 -169.1   1957    1.0\n",
      "\n",
      "Samples were drawn using NUTS at Wed Dec 19 11:20:18 2018.\n",
      "For each parameter, n_eff is a crude measure of effective sample size,\n",
      "and Rhat is the potential scale reduction factor on split chains (at \n",
      "convergence, Rhat=1).\n"
     ]
    }
   ],
   "source": [
    "print(fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the treedepth, E-BFMI, and divergences"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 of 4000 iterations saturated the maximum tree depth of 10 (0.0%)\n",
      "0.0 of 4000 iterations ended with a divergence (0.0%)\n"
     ]
    }
   ],
   "source": [
    "stan_utility.check_treedepth(fit)\n",
    "stan_utility.check_energy(fit)\n",
    "stan_utility.check_div(fit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot group mean distributions and matrix of probabilities that one mu is larger than other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix of probabilities that one mu is larger than other:\n",
      "[[0. 0. 0.]\n",
      " [1. 0. 1.]\n",
      " [1. 0. 0.]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# matrix of probabilities that one mu is larger than other\n",
    "mu = fit.extract(permuted=True)['mu']\n",
    "ps = np.zeros((3, 3))\n",
    "for k1 in range(3):\n",
    "    for k2 in range(k1+1, 3):\n",
    "        ps[k1, k2] = np.mean(mu[:, k1] > mu[:, k2])\n",
    "        ps[k2, k1] = 1 - ps[k1, k2]\n",
    "print(\"Matrix of probabilities that one mu is larger than other:\")\n",
    "print(ps)\n",
    "\n",
    "months = ['June', 'July', 'August']\n",
    "fig, ax = az.plot_forest(fit,\n",
    "                           kind='ridgeplot',\n",
    "                           var_names=['mu'],\n",
    "                           combined=True,\n",
    "                           ridgeplot_overlap=1,\n",
    "                           r_hat=False,\n",
    "                           n_eff=False,\n",
    "                           figsize=(7, 7))\n",
    "ax[0].set_yticklabels(months[::-1]) # Order of months if reversed, since arviz flips the order of ticks in plot\n",
    "ax[0].set_xlabel('Average temperature');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Common variance and hierarchical prior for mean.\n",
    "\n",
    "Results do not differ much from the previous, because there is only\n",
    "few groups and quite much data per group, but this works as an example of a hierarchical model.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "// Comparison of k groups with common variance and\n",
      "// hierarchical prior for the mean\n",
      "data {\n",
      "    int<lower=0> N; // number of data points\n",
      "    int<lower=0> K; // number of groups\n",
      "    int<lower=1,upper=K> x[N]; // group indicator\n",
      "    vector[N] y; //\n",
      "}\n",
      "parameters {\n",
      "    real mu0;             // prior mean\n",
      "    real<lower=0> sigma0; // prior std\n",
      "    vector[K] mu;         // group means\n",
      "    real<lower=0> sigma;  // common std\n",
      "}\n",
      "model {\n",
      "  mu0 ~ normal(10,10);      // weakly informative prior\n",
      "  sigma0 ~ cauchy(0,4);     // weakly informative prior\n",
      "  mu ~ normal(mu0, sigma0); // population prior with unknown parameters\n",
      "  sigma ~ cauchy(0,4);      // weakly informative prior\n",
      "  y ~ normal(mu[x], sigma);\n",
      "}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with open('grp_prior_mean.stan') as file:\n",
    "    print(file.read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    }
   ],
   "source": [
    "model = stan_utility.compile_model('grp_prior_mean.stan')\n",
    "fit = model.sampling(data=data, seed=194838)\n",
    "samples = fit.extract(permuted=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot group mean distributions and matrix of probabilities that one mu is larger than other. The probabilities are practically either 1 or 0 since the distributions are not overlapping almost at all. This can be visually seen from ridge plot below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix of probabilities that one mu is larger than other:\n",
      "[[0. 0. 0.]\n",
      " [1. 0. 1.]\n",
      " [1. 0. 0.]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# matrix of probabilities that one mu is larger than other\n",
    "mu = fit.extract(permuted=True)['mu']\n",
    "ps = np.zeros((3, 3))\n",
    "for k1 in range(3):\n",
    "    for k2 in range(k1+1, 3):\n",
    "        ps[k1, k2] = np.mean(mu[:, k1] > mu[:, k2])\n",
    "        ps[k2, k1] = 1 - ps[k1, k2]\n",
    "print(\"Matrix of probabilities that one mu is larger than other:\")\n",
    "print(ps)\n",
    "\n",
    "months = ['June', 'July', 'August']\n",
    "fig, ax = az.plot_forest(fit,\n",
    "                           kind='ridgeplot',\n",
    "                           var_names=['mu'],\n",
    "                           combined=True,\n",
    "                           ridgeplot_overlap=1,\n",
    "                           r_hat=False,\n",
    "                           n_eff=False,\n",
    "                           figsize=(7, 7))\n",
    "ax[0].set_yticklabels(months[::-1])\n",
    "ax[0].set_xlabel('Average temperature');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unequal variance and hierarchical prior for mean and variance\n",
    "\n",
    "Results do not differ much from the previous, because there is only\n",
    "few groups and quite much data per group, but this works as an example of a hierarchical model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "// Comparison of k groups with unequal variance and\n",
      "// hierarchical priors for the mean and the variance\n",
      "data {\n",
      "  int<lower=0> N; // number of data points\n",
      "  int<lower=0> K; // number of groups\n",
      "  int<lower=1,upper=K> x[N]; // group indicator\n",
      "  vector[N] y; //\n",
      "}\n",
      "parameters {\n",
      "  real mu0;                 // prior mean\n",
      "  real<lower=0> musigma0;   // prior std\n",
      "  vector[K] mu;             // group means\n",
      "  real lsigma0;             // prior mean\n",
      "  real<lower=0> lsigma0s;   // prior std\n",
      "  vector<lower=0>[K] sigma; // group stds\n",
      "}\n",
      "model {\n",
      "  mu0 ~ normal(10, 10);       // weakly informative prior\n",
      "  musigma0 ~ cauchy(0,10);    // weakly informative prior\n",
      "  mu ~ normal(mu0, musigma0); // population prior with unknown parameters\n",
      "  lsigma0 ~ normal(0,1);      // weakly informative prior\n",
      "  lsigma0s ~ normal(0,1);     // weakly informative prior\n",
      "  sigma ~ cauchy(lsigma0, lsigma0s); // population prior with unknown parameters\n",
      "  y ~ normal(mu[x], sigma[x]);\n",
      "}\n",
      "\n"
     ]
    }
   ],
   "source": [
    "with open('grp_prior_mean_var.stan') as file:\n",
    "    print(file.read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using cached StanModel\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:pystan:1 of 4000 iterations ended with a divergence (0.025%).\n",
      "WARNING:pystan:Try running with adapt_delta larger than 0.8 to remove the divergences.\n"
     ]
    }
   ],
   "source": [
    "model = stan_utility.compile_model('grp_prior_mean_var.stan')\n",
    "fit = model.sampling(data=data, seed=194838)\n",
    "samples = fit.extract(permuted=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot group mean distributions and matrix of probabilities that one mu is larger than other:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "std(mu0): 2.55\n",
      "Matrix of probabilities that one mu is larger than other:\n",
      "[[0. 0. 0.]\n",
      " [1. 0. 1.]\n",
      " [1. 0. 0.]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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ktnbv3ol165Kh8QmCV+9HAQAqgzcCYyYDAP4+YzosFovIiG6FpegE2dlZGDt2FK5evQLfrsOh63C/6EhCSZIKQbGvwNTuPuRdzkJMXAxOnjwhOhaRW5oz51MAQOB9T0KlNVS/bgjrDn2zTriRewmff/udqHhuh6XoYGlpexETMwRnzmTAKzwKDYa+4PGXYNSFpNYgaNSfYWo/ENdyszE85n5s2ZIqOhaRWzl//hzWr0+G2uQLXbuBNZZJkoQG0U8CAD6b8xmPLdYRS9FBiooKMX36/yEubjiys7Pg03EQAh+aCkmjFR3NZUgqNYJGvQbf3mNRWlyIx8eNxYcfzYLVahUdjcgtLFmyEDabDQ0iH4BKq//Vcn3zztAGNUfehVPYvGOXgITuh6VoZ2azGV98MRtRUV0we/bHkDR6hIz4A/xjX2Mh3oQkqeA/6FkExEwGJAlv/3M6RsaNwOHDh0RHI3Jpsixj5cplAAB9+8E3fY8kSfCJHAkA+NfHnzktmzvjdYp2UlRUhIULv8Xnn3+GzMxLAACfDgPhO+AZaPxCnJbDnZXnnkXemv+g/Mo5SJKEB0aOwqTf/wG9e/fllDPRLxw4kIaYmCHQNwpHo2c+vOX7bOYSXPrsN4DNimNHTyEoMNCJKV1TbdcpqqdPnz7dGSHGjx+P/Px8dO/e3RnDAQBKSsodun1ZlnHo0AHMnv0xJk+ehLVrk1BYeAOmVj0Q/NAUeHePg8rgOc9IdDS1lz+8uwyHyuSH8uxTOHX8MBYvXoBVCStxJfcyGjRogODgEBYkEYDPPvsI+/enVV6XGHrr+ydLGi0sBTkoz0mHzTsIg/v1cWJK1+Tl9eup5ipO21McP348Bg0ahOeee84ZwwGwz56i1WrFhQvnUVpaitLSEmRlZeH8+XP48ceD2Lt3N7KzswAAkkoF7/b3wTvqYegatr7nces7W0UZio9tQfHBJJhz/3fJRoMG/ujVqze6d++JFi1aokmTpvDx8YXJZILBYIC/fwAMBkMtWyZyfxaLBV27tsOVq1fQ5IX50PjUvvdXdvEoLi+agpDWnXF01w4npXRdte0papyYAwCwZ88eTJo0CQcPHqx+bcqUKTCZTJg2bRouXbqE+++/H++++y7mzJmDvLw89O/fH++88w5MJhMA4OLFi3j77bdx6NAh6HQ6jB49GpMnT4ZGY/8fZ8KEJ7F+/dpbLtc3ag3fjoOgi7gPGp8gu49fX6m0Bvh0i4FPtxhU5F1EyaldKMvYg4Ls09iwYR02bFh30/UCAoOwP+0IvLy4h06ea/v2rbhyJRemll1vW4gAoG/aAWqfYORmHMHJ0xmICOcv7rfi9FKsq82bN2PlypUoLy/Hk08+icWLF+O5555DWVkZJkyYgMcffxwfffQRCgoKMGnSJPj6+jpkLzQ39zIg/ex8JEkCJFXlFJ5KjfJrWbi6bRGwbZHdx6ZfkzQ6wGaDLNsAWQYgK/+tdN2iRlaxDW3YieTBqk6w8eowqE7vlyQVvDoOxI3dK/DBV9/i83dnODCde3PZUnzxxRfh41O5iztkyBAcO1Z5n8zNmzfDaDTi+eefBwCEhITgt7/9LT7//HOHlGJ4eFv8dPIkbB57OpIbUt/6pOl23aLQpIHJiWGInKu0tBRJSashqbUwtOlb5/W8OgzGjd0rsH5NPOR33uKx+Vtw2VIMDg6u/rPJZEJxcTEAIDMzE2fPnkXPnv975JLNZnPYcaTPPvsCn/FMZiJyERs3rkdRUSG8I/pBZfCu83q64BbQhoShOPcstu/Zh/v69HJgSvfl9FI0mUwwm82w2WxQqSp/48/NzUXLli3rtH5oaCgiIiIQHx/vwJRERK5pxYrKqVNT+4G3eeeveXUYiILcs5i7YAlL8RacfvF+WFgY9Ho9EhMTYbPZsHHjRuzbt6/O6w8aNAjXr1/H/PnzUVpaCpvNhgsXLmDnzp0OTE1EJN716wXYtGkDVHoT9K3u/AHlprbRAIDtqcm87dstOLUUJUmCt7c3Zs6ciY8++ghRUVFITU3F8OHD67wNk8mE+fPn48CBAxg6dCiioqIwefJkZGVlOTA5EZF4a9cmoby8HD5t+970tm63o/VvDG1IGEquZmH3Ad416macNn1aVFQEf//KJ0DHxsYiNjb2pu9r2rQpTp48WeO1yZMn1/i+WbNm+Pjjjx0TlIjIRX3//SoAgKFd/7vehqltP1zPPYsvFi5F3x6R9ormMZyyp3jixAmkp6ejc+fOzhiOiMjjFBTkY8uWVKgM3tC36HbX2zFFVE6h/rDx1tdf12cOL8Vp06bh+eefx6uvvorw8HBHD0dE5JHWrk2CxWKBT0RfSOq7f7iALqg5NAFNUZRzFgePHrdjQs/g8FKcMWMGtm7diokTJzp6KCIij5WYWHnGvb7t3U+dVqnaW5y7cOk9b8vT8NFRREQu7tq1PGzdugUqgzcMLbre8/a8IvoBAFI3JN3ztjwNS5GIyMVVTZ36touGpL738yO1Ia2g8WuIgouncDLj7O1XqEdYikRELq566rRNP7tsT5Kk6inULziFWgNLkYjIheXl5WHbth+gMvpAb4ep0yqmtpX3Td2wIdlu2/QELEUiIhe2bl0SrFYrfCL62WXqtIqucVuoTH64nH4YuVeu2m277o6lSETkwqqeHaoP72PX7UoqNYytowDZhvkrv7frtt0ZS5GIyEWVlZXhhx82Q9LooW/exe7bN4VX3hT8+2SehVqFpUhE5KJ27tyGkpJimMK63tW9Tm/H0DISUGtw+sAOmM1mu2/fHbEUiYhcVNXUqbF1lEO2r9IZYWjRFbbyEqxcv8khY7gbliIRkQuSZRkpKesBAPpWjilFADCF9wYALF3F44oAS5GIyCWdOPETLl68AH3D1tD4BDlsHGPryuOKB3am8hmLYCkSEbmklJTKqVPvNr0cOo7GNwi6hq1hzs/Brv18xiJLkYjIBVUdT9SG9XT4WFV7i/NWJDh8LFfHUiQicjF5eXlIS9sLtakBdI3bOHw8Y5vK44pbUzc4fCxXx1IkInIxqakpsNls8GkTBUly/D/TuoatofYOQP6547iYle3w8VwZS5GIyMVUHU/UOvCs05+TJAnG8F4AZHy9rH5PobIUiYhcSEVFBVJTN0FSa2Fo0c1p4xqVSzPWrqvfNwhnKRIRuZA9e3bhxo3rMLboDJXe5LRxDc27QNLoce7IbpSUlDhtXFfDUiQiciFVZ516OeguNrei0uphCIuEXGHG0qT6e8INS5GIyEXIsoy1a9cAcN7xxJ+rujRjReJqp4/tKliKREQu4tixozh//hz0DVtD26CR08c3hUcBkPDj7vp7dxuWIhGRi0hKqrz/qG/7aCHjq738oWvcFuU38rB1zz4hGURjKRIRuYjk5MppS01r+z5Q+E5UPWPx2+WrhGUQiaVIROQCzpw5jZ9+Og5dQBNoA5sJy1F1d5ttqeuFZRCJpUhE5AKSkipPsPFpFw1JkoTl0Aa1gMavIa5nnsbps2eF5RCFpUhE5AKSkyuPJ+rbiJs6BZS72ygZvlkaLzSLCCxFIiLBsrOzsH9/GrS+QdA0dPwNwG/HpEyhrltf/+5uw1IkIhIsObly6tQ7op/QqdMq+qYdoTL44NJPB1BQkC86jlOxFImIBKs669QQLnbqtIqkUsPYuidgs2LBqvp1IT9LkYhIoLy8POzcuR0akx+0TTuKjlOt6rhi/PcsRSIicpING9bCarXCq01vSCq16DjVjGHdAbUGP6Vtg9lsFh3HaViKREQCVU2dGtv2FZykJpXOCEOLrrCaS7AmZZPoOE7DUiQiEqSoqBBbtqRCpTdB17yr6Di/YlKmUBfG158HD7MUiYgE2bQpBWazGV6toyBpdKLj/ErVUzP2bdtYb24QzlIkIhKk6gbgJhebOq2i8QmErnFbmK9fxdbde0THcQqWIhGRAGVlZUhJ2QBJo4UurIfoOLdkiugHAPhiwRLBSZyDpUhEJMC2bVtQXFwEU1h3qHRG0XFuyav9AADAtg2rYbPZBKdxPJYiEZEASUmVZ516Rbjm1GkVjW8I9E06oOz6FaRs+UF0HIdjKRIROZnFYsG6dUmASgVdq16i49yWV4fKvcW53y0SnMTxWIpERE62e/dOXLt2DcZmnaE2+oqOc1umiP6ApMKezWtRUVEhOo5DsRSJiJys6qxTb+UkFlen9moAQ4uuqCi5gRVr1oqO41AsRSIiJ7LZbJXHEyUJuvDeouPUmVenIQCAz+fNE5zEsViKREROtHfvHuTkZMPQpAM0PkGi49SZqW0/qPRe+GnvFuRczhEdx2FYikRETrR69SoAgG+H/oKT3BmVVg+vjoMBmxX/mfu16DgOw1IkInISm82G1asTAQDacNe+FONmvLvFAABWLl3gsdcsshSJiJxk3769lVOnTd1r6rSKLrgldI0jUHQlE+tSU0XHcQiWIhGRk1RPnbZ3r6nTn/PpNgIA8P7HnwlO4hgsRSIiJ7BYLEhMXAVIErTh7nEpxs2Y2g+EyuiLY7tTcfpMhug4dsdSJCJygh9+SMXlyzkwNu8Cja/7TZ1WUWn18IkcCUDGjH9/KDqO3bEUiYicYMmSyluk+XYZKjjJvfOJjAXUGqSsXobr1wtEx7ErliIRkYMVFORj3bokqHRG6NzwrNNfUnv7w6vDIFjNpXjvs7mi49gVS5GIqp07dxbvvfc2pk//P+zYsU10HI+xcuVymM1m+LSLhkpnEB3HLnyjRgMA/vv1HJSUlAhOYz8sRSICAGzcuB4DB/bBv//9LmbP/hhjxsTi5Vf/5PE3gHY0m82GL7+cAwAwdo0RnMZ+dMEtYWzbF+bCa/jP7Dmi49gNS5GIkJWVieefn4jS0lIE9BmLgGGToDL6YtGCefjTn18THc+tpaSsx5kzGTA0aQd9aDvRceyqQfSTAIAv53zsMXuLLEUiwtSpr6OoqBD+UQ/BZ+Cz8Okeh0bj/wOV0RcrFs/HwqVLRUd0W3PnVl7P16DXGMFJ7E8XEgZT234oK8zHvz+bLTqOXbAUieq548ePITl5NTS+QfDu/3T161r/xgiKq9xL/NubU1FcXCwqotvatWsHtm/fCq1fQ+jC+4iO4xB+/Sv3Fr+Y/REKCvIFp7l3LEWieu6bb74EADToOQoqnbHGMmOrHjC26YOSgit469+zRMRzW7Is4x//+DsAIOC+JyGp1IITOYYuuCW8Og1BefF1vDF9hug494ylSFSPFRUVYfnyJZA0Whg63vz6Of+BzwCQsOjbr1BWVubcgG5s2bLFSEvbC11wC+jbDxIdx6EaDHgGktaAhCXzceLkSdFx7glLkageS01NQWlpCbzb9oHa5HfT92gDm8HYpjfKi/Lx0Vee/YBZe8nNzcXf/z4VABA0bJLH7iVW0fgEwq/Po5BtVkyY9HtYrVbRke4aS5GoHktOXg0AMLap/YLyqmvS5n/LUrwdm82GyZN/j2vXrsGv63Bom3UWHckpfHs/DG1wS5w5dgCzPvlEdJy7xlIkqqfKy8uRkrIBkloLfVjPWt+rb9oRmoAmyDt/AnsOHHRSQvc0Y8Y0bN68CbqAJvAd8jvRcZxGUmsRFPsqoFLjP+/NRFraPtGR7gpLkaie2rdvDwoLb8DUogtUelOt75UkCd6dhwEAZnnwU9fv1eeff4rZsz+G2uCFkDF//dWJS55O17AVGgx4BjZLOR578jFkZl4SHemOsRSJ6qlt234AAJjCIuv0fq+OgwAAOzYleexT1++WLMv4z3/+hWnTpkKl1qLR2DehDmopOpYQvr3GwKvzUBQV5OGBUSNx8eIF0ZHuCEuRqJ7avn0rAEDTrEud3q/xCYK+SXuU38hDytYdjozmVoqKivDHP/4e//rXP6HSGdDo0WnQNO0kOpYwkiQhcMSLMLaOQs6lcxg4uD+Sk9eIjlVnblGKEREROHLkiOgYRB6jqKgIBw6kQWX0gTakZZ3XM7WtfDju14uXOSiZezl8+BBGjBiE5cuXQOMdgNBx/4S2Rd32vD2ZpNYieMzf4N3tARTdKMCECU/i8XFjceBAmuhotyWsFMePH4+vv+axCSIR0tL2wmKxwKt5Z0hS3f8ZMEVEAwB2b1kHWZYdFc/lZWVl4i9SqNbcAAAf+0lEQVR/eQXDhg1EevopmMIi0WjCR1A3jhAdzWVIag0CR7yI4DF/g8YnCJtTUxATMwSDh/THvHlfuezdbzSiAxCR8+3fX3lmoL5J+ztaT+MXAl2jNijLSccPu/diUN/ejojnkoqKCrFjx3asWrUCq1cnoKKiAmq9CYEDx8PQLfaOfrmoT0xt+8LYqgcKf1yP4oPJOHb0MN5441VM/dvrGDBgEB4cNRrDhsUgJCREdFQALlCKe/bswaRJk3Dw4P9O854yZQpMJhOmTZtW473Xrl3DgAEDkJSUhBYtWgAALBYLBg4ciHfffRf33XefU7MTuauqaSx1ozZ3vK6pbV+U56Tj2xUJbl+KWVmZ2LQpBRaLBTabFVarFVarDTabDVarFUVFhbhw4RxOnjyJn346Vn2CkUpnRECfB2HqORpqL3/BP4XrkzQ6+PYYBZ/ucTBnHkfx4RSUpO/G5tSN2Jy6EQDQunUb9O3bDxER7dC8eUsEBgbBy8sLJpMJKlXlLxxBQcHw8vJyaFbhpXgnAgICMGTIEMTHx+OVV14BAGzduhVarRbR0dGC0xG5B1mWK0tRUkHXKPyO1zeG90LB1v9i++YNAN6xf0AnGjVqxJ2dHalSQ1KpIQPIP5CM/APJDstWH0gaPWSbBbDZkJGRjoyM9Frfr9XpcDr9IoxGx13q4nb7+48++igSExOrf2OLj4/H6NGjq3+TIKLanT9/Dnl5edCHtIRKe+dPgdcGtYDaNxjXL6Xj7IWLDkjoPB06dISk1gK1fEkaPSStAZLOCEmjAzz8lm1OpVJB0ugg6QyVn7FGV/m5q9SVX5KqxpfsFYRCi+TQSG61pwgA0dHRUKlU2LlzJzp06IAtW7bgjTfeEB2LyG1UTZ0am9zdA28lSYIpvBcKDyTh62UJmPnnyfaM51TffbcUsiyj/p4y5H5UkmNLUfjulclkgtlsrnExcG5u7i3fr1Kp8PDDDyM+Ph7ff/89IiMj0axZM2dEJfII1ccTG9758cQqxta9AADr1q+1SyaRJEmCil9u8+VowksxLCwMer2+ekp048aN2Lev9nvmjR07Fps3b8aSJUswduxYJyUl8gz791eWoi707i8fMDTvDElrwMVje1HEhw+TBxFaipIkwdvbGzNnzsRHH32EqKgopKamYvjw4bWu17hxY/To0QNXrlxBTEyMk9ISub/y8nIcPXoYKr0J2sCmd70dSaODoWU3yJZyLE1ab8eERGIJO6ZYVFQEf//KU5ljY2MRGxt7y/eevMlDK5s2bYrQ0FAYDHd+ogBRfXXs2BGYzWaYwrrd83V1xta9UJq+G/HfJ+G5xx62U0IisYTsKZ44cQLp6eno3PnunjOWmZmJNWvW4Mknn7RzMiLPduDAfgCAoXHbe96WqXUUAODH3Zvr9d1tyLM4vRSnTZuG559/Hq+++irCw+/8Gqnp06cjLi4OTz/9NNq1u7uz54jqq/9dtH/vpaj29oeuURuU37iK3QcO3fP2iFyBJHvwr3hXrhSKjkDkUvr27Y6MjNNo+uJ3UHvf+51YCrYtwPWdS/DY7/+CT//xph0SEjlecLDPLZcJP/uUiJyjoCAfGRmnofENtkshAoAhrAcA4Ictm+yyPSLRWIpE9UTV8UTTXV60fzP60LZQ6b1wOf0wCm7csNt2iURhKRLVE1XHE3Wh9348sYqkUsMQ1h2wWbD4+3V22y6RKCxFonrCnifZ/JwxrDsA4Pt1LEVyfyxFonpAlmUcPLgfUKmga9jarts2tKo8rnh07zZemkFuj6VIVA+cPXum8skYwWF39WSM2mi8A6ANCYO54DL2Hzlu120TORtLkageSEvbCwAwNWvvkO0blbNQF6xa7ZDtEzkLS5GoHqgqRU2ju78JeG2MyhTqls28NIPcG0uRqB5IS6t88ow21DF3gdI3aQdJZ0T2yQN8aga5NZYikYcrKirC8eNHoTb5QdOgkUPGkNRaGFp0hWytwMp13Fsk98VSJPJwhw4dgM1mg7Fpe0gOfEirsWUkAGD1ho0OG4PI0ViKRB6u6niisaljTrKpYmjRFQBwaO92h45D5EgsRSIPt2/fHgCAykEn2VTRBDSB2jsQNzJPI/vyFYeOReQoLEUiDybLMvbv3wdJpYau0Z0/qu1OSJIEQ8vKvcXFa9Y7dCwiR2EpEnmwM2dO49q1a9CF2P+i/ZupmkJdn5rq8LGIHIGlSOTBdu3aCQDwat7RKeNVleJPB3Y5ZTwie2MpEnmw7du3AgDUTTs5ZTyNTxA0AU1RlpeJkxnnnDImkT2xFIk8lCzL2LlzOyBJ0DupFIH/7S0uWr3WaWMS2QtLkchDnT2bgZycbOhCwqA2+jhtXKNSiqlbtjhtTCJ7YSkSeajt27cBALxbdnHquPrmnQFIOHN4Dx8lRW6HpUjkoXburCxFTdPOTh1XbfSBrlFrVBRdw94fjzp1bKJ7xVIk8kA2mw3btm0FJBV0TZ1z5unPVR1XXLZmndPHJroXLEUiD3T06GFcuZILQ2hbqA3eTh/f0KIbAGDbth+cPjbRvWApEnmg1NTKm3J7t+4pZHx90/aAWoMLx9NgsViEZCC6GyxFIg+0aVMKAEDTIlLI+CqtAfomHWAzl2Dzrr1CMhDdDZYikYe5fr0AaWl7oTb5Qte4jbAcVZdmrEzmfVDJfbAUiTzM1q1bYLVa4RXWHZIk7q941ck2u3ZsFZaB6E6xFIk8TNXxREOrHkJz6Bq3gaQzISf9MIqLi4VmIaorliKRB5FluboUdYKOJ1aRVGoYmneGbK1A8uZtQrMQ1RVLkciDHD58CNnZWdA3bgu1VwPRcWBoWXlpRuK6DYKTENUNS5HIgyQnrwYA+ET0FZykUtVxxbTd3FMk98BSJPIgyclrAAC61n0EJ6mkDWwGtXcArl04hbxreaLjEN0WS5HIQ2RkpOPkyRPQBjSFNqiZ6DgAAEmSlL1FGcuTU0THIbotliKRh0hKqtxL9G3XT3CSmqqmUNdu3CQ4CdHtsRSJPMTatZWlqG3dW3CSmqpK8cd9OwQnIbo9liKRB8jJycb+/fug9g4Uehebm9H4BkMT0AQlVy7hzLnzouMQ1YqlSOQBvv9+FQDAt30/oXexuZWqp2Z8u2qN4CREtXO9vz1EdMdWrVoBANC3HSA4yc2ZlKd1bNjA5yuSa2MpErm58+fPYf/+NGh8g6FrEiE6zk3pm3eBpNHj7OHdKCsrEx2H6JZYikRuLjExHgDg13GgS06dAoBKq4ehZTfYKsxI3MCzUMl1uebfICKqs1WrVgIAdBH3CU5SO2PrKADA0oTvBSchujWWIpEbO3XqJI4dOwJtQBNoQ1qJjlMro3JcMW1HKmRZFpyG6OZYikRubOnSRQCqpk4lwWlqp/EJgq5ha5TlX8b+H4+IjkN0UyxFIjdlsVgqS1GSoO94v+g4dWJs3QsA8PXSlYKTEN0cS5HITW3cuAG5uZdhbNEVGr+GouPUiUl5esfGtYmCkxDdHEuRyE0tWvRfAIBf1+GCk9SdNjgMmoCmuJ51Bj8eOyY6DtGvsBSJ3NDlyzlISVkPtcEbunDXeExUXUiSBK/2lWfJzv52oeA0RL/GUiRyQ0uXLoLVaoVvp8GQNDrRce6IV7vKu+6kJCfyLFRyOSxFIjdTUVGBr7/+AgBg6DJCcJo7pw1qBm1IGIpyL2Lrrt2i4xDVwFIkcjPff78K2dlZMIV1hy64peg4d8W78zAAwAeffyE4CVFNLEUiNyLLMubM+RQA4NdrtOA0d8+r42BArcXuTUkoLLwhOg5RNZYikRvZvXsnDh8+BF1Qc2hbRIqOc9fURh94tesPW0UZZs9fIDoOUTWWIpEb+eSTDwAA/r3HuPwdbG7Hu2vl8dCvv54Lm80mOA1RJZYikZtIS9uLjRs3QOMTCH27gaLj3DN9047QNWqDgqyzWJHIm4STa2ApErmJ9957GwAQGD3O7S7DuBlJkuDX91EAwNvvv8fLM8glsBSJ3MDOnduxZUsqtH4h0HcaKjqO3Rjb9IE2sBmyTh9F0oYNouMQsRSJXJ3VasXf/vYGACBgwNOQ1FrBiexHklTw6zcOAPD61CmwWCyCE1F9x1IkcnHffTcfx44dgSG0LfTtB4mOY3em9gOgb9IBVy9m4NO5c0XHoXqOpUjkwi5fzsE778wAAAQM/T0kyfP+ykqSBP+hzwOQ8P77byMrK1N0JKrHPO9vGJGHkGUZr732EvLz8+EX+QC0jSNER3IYfaNw+HQfiYqSQjz13EReokHCsBSJXNTChf/Fhg3roG3QCL4DnxUdx+EaDJoIbWBzHNu/CzPffVd0HKqnWIpELmj//n2YMuU1SJIKIbEvQ6U3iY7kcCqtHkEP/gWSRo9PP3wXS5YtER2J6iGWIpGLuXDhPJ599mmUl5cjaMhEaJp2Eh3JaXQhYQh68HVAUuHlP/0Bid8niI5E9QxLkciFXLhwHg8/HIecnGz4dB4CY4+HREdyOlOb3ggY/gfYrBY8/7sJ+OrrL3hhPzkNS5HIRezZsxuxscNw4cJ5eLeLhv+Il9z+/qZ3y6dbDALjXoMsSZj61z9j4m8nID//muhYVA+wFIkEKykpwbvv/gNjxozE5cs58O18PwLi/gJJrREdTSjvjoPRcNw/ofEJQtLqVegR1RWff/4piooKRUcjD1bnUpw+fToiIiJw8OBBR+apsz179iAy0n0fnUNUUJCPTz75EH37dsesWe/DBgkhI15AgwderveFWMXQrBMaPfsxvDoPRdGNG5g2bSo6dY7An/70ByQnr2FBkt1Jch0m68vKytC/f3+o1Wrcf//9ePvtt52RrVZ79uzBpEmTai3pK1f4F4Zch9VqRXr6Kezbtwfr1ydj69YtKCsrAwB4temNBoN/C41/Y8EpXVf55Qzc2BuP4hM7AFvl7eAkSULr8Dbo2qUb2rRpi5Ytw9CiRUs0bhwKf/8AGI1GwanJFQUH+9xyWZ1KMSEhAW+//TamTp2Kt956C9u3b4eXl9dNi2nKlCkwmUyYNm0aACAtLQ1vvfUWLl26hJ49e6J58+a4dOkS5iq3c4qIiMCKFSvQuXNnAEB8fDy++eYbrFmzBgAwf/58fPvttygoKICfnx8mTJiAhx56CAMHDoTZbIbJVHmq+meffYZ+/frVyM1SJGeRZRkxMYNx9OiRGq9V/VeW5ZtfkK5SV97LtJ4eO7wrsgzINsg2K2CzAaj9n7BfHpf9+ffR0fdh5crVjkhJLqy2UqzT9Ony5csxcuRIjBw5ElqtFsnJyXUa+Pr165g0aRKeeOIJ7Nu3D8899xzi4+PrlhrA2bNn8cEHH+Crr77CwYMHER8fj6ioKPj7++PLL7+EyWTCwYMHcfDgwV8VIpEz5edfw8GDB1BRUVH9ZbFYYLFYYLVa/1eIkgpQaSBpdJB0xspHQLEQ74wkVf4yodFB0hkgaQ2Vn6NaC6g0lZ+xpAJQ+blW/VLy819Oqr5OZV4R+7OQy7ntgYuzZ88iLS0Nr7/+OnQ6HUaOHIkVK1bg0Ucfve3GN2/ejMDAQDz55JMAgD59+mDIkCEoKiqqWziNBrIsIz09HaGhoQgICEBAQECd1iVypoCAQKz6PgUfJu1DVlEFVCo11BoNtFot/PwDENKwMZo3DEKgl77q32pyBhkos1hRWl4Bs7kCFZYKWC0VkGVApVZjZLcw0QnJxdy2FJcvX45WrVqha9euAICHH34Yjz76KNLT02+78dzcXISGhtZ4LTQ0FKdOnapTuGbNmuG9997DokWLMHXqVHTu3BmvvfYaunTpUqf1iZwpuk9vRPfpLToGEd2DWkuxoqICiYmJKCwsRHR0dI1lK1asQFxcHMxmM2w2G1SqypnY3NxctGzZEgAQEhKC7OzsGutlZWXV+N5kMlWfbFC1/s/FxMQgJiYGZrMZX375JV566SVs2bKlejwiIiJ7qbVZNm/ejOvXryM+Ph4JCQnVX6+//joSExMRFhYGvV6PxMRE2Gw2bNy4Efv27atef9CgQbhy5QqWLFkCi8WCvXv3YvPmzTXG6NChAxITE2GxWJCeno5ly5ZVLztz5gy2b9+OsrIyaLVaeHl5VZdhYGAgSktLceUKjwkQEZF91FqKy5cvR1xcHMLDwxEcHFz9NW7cOFitVmzduhUzZ87ERx99hKioKKSmpmL48OHV6zdo0ACzZ8/GwoULERUVhS+//BJxcXHQ6XTV73nzzTdx7NgxREVFYcaMGRg7dmz1soqKCnzyySfo168foqKisH79esyaNQsA0KpVKzz22GOIi4tDz549sWvXLnt/NkREVM/U6ZIMe3r55ZcREhKCqVOnOnwsXpJBRES/dM+XZNyLbdu2IS8vD1arFZs2bcLGjRsxcuRIRw9LRER0xxx+L6njx4/j9ddfR2lpKUJDQzFz5kx069bN0cMSERHdMadPnzoTp0+JiOiXhE6fEhERuQuWIhERkYKlSEREpGApEhERKViKRERECpYiERGRgqVIRESkYCkSEREpWIpEREQKliIREZGCpUhERKRgKRIRESlYikRERAqWIhERkYKlSEREpGApEhERKViKRERECpYiERGRgqVIRESkYCkSEREpWIpEREQKliIREZGCpUhERKRgKRIRESlYikRERAqWIhERkYKlSEREpGApEhERKViKRERECpYiERGRgqVIRESkYCkSEREpWIpEREQKSZZlWXQIIiIiV8A9RSIiIgVLkYiISMFSJCIiUrAUiYiIFCxFO4iMjKzx1bFjR4waNUp0LJeTm5uLyZMno3fv3ujduzf+8Ic/ICcnR3Qsl3Px4kVMmjQJvXv3Rr9+/fCf//wHNptNdCyhkpOT8cQTTyAyMhJDhgypscxisWDmzJno1asXevbsialTp8JsNgtKKk5tn1Fty6gmlqIdHDx4sMZXq1atEBsbKzqWy3nrrbdQUVGBTZs2YcuWLTAajZg6daroWC7FarXihRdeQMuWLbFt2zasXLkSP/zwA7766ivR0YTy8/PD008/jZdffvlXyz7//HPs2bMHq1evxoYNG5CRkYH3339fQEqxavuMaltGNbEU7ezw4cPIyMjAmDFjREdxORcuXEBMTAy8vb1hNBoxatQonDx5UnQsl3L27FlkZGTg5Zdfhk6nQ+PGjTFhwgQsWbJEdDShoqOjERsbiyZNmvxq2YoVKzBp0iQ0bNgQAQEB+OMf/4j4+HhYrVYBScWp7TOqbRnVxFK0sxUrVmDAgAFo2LCh6Cgu59lnn8W6detw48YNFBUVITExEYMHDxYdy6XIslz99fPXMjMzUVRUJDCZa7px4ways7PRrl276tc6duyI4uJiZGZmCkxG7oqlaEclJSVISkrCI488IjqKS+rRowcKCwvRq1cvREVF4ezZs3j11VdFx3IpYWFhaN68OWbNmoWysjJcvHgR8+fPBwCW4k0UFxcDAHx9fatf8/HxqbGM6E6wFO1o3bp1MBqNGDRokOgoLsdms+HZZ59Fp06dsH//fhw8eBBDhw7F+PHjUVFRITqey9BoNJgzZw7Onj2LwYMH43e/+x0eeughSJJU4x9+quTl5QUAKCwsrH6t6s9Vy4juBEvRjpYvX47Ro0dDo9GIjuJyCgoKkJmZifHjx8PLywsGgwETJkzA6dOnceHCBdHxXErr1q3x1VdfYdeuXdW/aHXu3Bkmk0l0NJfj6+uLxo0b48SJE9WvHT9+HF5eXjx+RneFpWgnZ86cwcGDBzl1egsBAQFo0aIFFi5ciLKyMpSXl+O///0v/Pz80LRpU9HxXMqJEydQXFwMi8WCHTt2YM6cOfX+rEGr1Qqz2YyKigrIsgyz2Yzy8nIAwCOPPIK5c+fi8uXLuHbtGj799FM8/PDDUKvVglM7V22fUW3LqCbeENxO3nvvPRw+fBgLFiwQHcVlnT59Gu+88w6OHj0Km82GNm3a4M9//jO6d+8uOppL+fDDD7F48WKYzWa0atUKL730Ur2fko+Pj8df//rXGq81adIEqampsFgsePfdd5GYmAibzYYRI0Zg2rRpMBgMgtKKUdtnVNsyqomlSEREpOD0KRERkYKlSEREpGApEhERKViKRERECpYiERGRgqVIRESkYCkSEREpWIpU74wfPx5RUVEec0eP8ePHY/ny5aJj2EV8fDyeeOIJ0TGoHmMpUr1y6dIlpKWlQZIkbNq0ySFjWCwWh2zX3Tnjc+FnT/eKpUj1SkJCArp27YoxY8YgISGh+vUff/wR0dHRNR5Mm5KSglGjRgGofMrHF198gaFDh6J3797405/+hIKCAgCVRRsREYHly5dj0KBBeOaZZwAAL730EqKjo9GjRw889dRTSE9Pr952fn4+Jk2ahO7du2Ps2LH44IMPauwhZWRk4Nlnn0WvXr0wYsQIJCcn3/Tn+eCDD5CWloYZM2YgMjISM2bMuO36U6ZMwfTp0/Hb3/4WkZGRGDduHK5cuYJ//vOfiIqKQkxMDI4fP179/iFDhmDu3LkYOXIkoqKi8Ne//hVms7l6+ebNm/HQQw+hZ8+eGDduXI2bcw8ZMgRffPEFRo0ahW7dusFisVR/jpGRkRg5ciRSUlKqM//973/HoUOHEBkZiZ49ewL49Z7wL/cmIyIisHDhQgwfPhzDhw+/o8+P6Fdkonpk6NCh8oIFC+QjR47IHTp0kK9cuVK97P7775e3b99e/f3kyZPluXPnyrIsy/Pnz5cfffRROTs7WzabzfKbb74pv/LKK7Isy/LFixfltm3byn/5y1/k4uJiubS0VJZlWV6+fLlcWFgom81meebMmfKDDz5Yve2XX35Zfvnll+WSkhI5PT1dHjBggDxu3DhZlmW5uLhYHjBggLxixQq5oqJCPnbsmNyrVy85PT39pj/T008/LS9btqz6+9ut/8Ybb8i9evWSjxw5IpeVlcnjx4+XBw8eLK9atUq2WCzyrFmz5Keffrp6e4MHD5ZjY2PlrKwsOT8/X3788cflWbNmybIsy8eOHZP79OkjHzp0SLZYLHJ8fLw8ePBg2Ww2V6/74IMPyllZWdWfS3JyspyTkyNbrVY5KSlJ7tq1q3z58mVZlmV55cqV1Z/DrX6+X76nbdu28oQJE+T8/Hy5tLT0jj8/op/jniLVG2lpacjKysIDDzyATp06oVmzZlizZk318tjY2Orvi4qKsHXrVsTGxgIAlixZgldeeQWNGjWCTqfDH//4R6xfv77GdN3kyZNhMpmqb0T9yCOPwNvbGzqdDpMnT8aJEydQWFgIq9WKDRs2YPLkyTAajQgPD8fo0aOrt7NlyxY0adIEY8eOhUajQYcOHTBixAisW7euTj9nXdYfNmwYOnXqBL1ej2HDhkGv12P06NFQq9UYOXIkfvrppxrbfOqpp9C4cWM0aNAAL7zwApKSkgAAS5cuxeOPP46uXbtCrVZjzJgx0Gq1OHToUPW648ePR+PGjas/lwceeAANGzaESqXCyJEj0aJFCxw+fLhOP9utPP/882jQoAEMBsM9f35Uv/HBf1RvJCQkIDo6GgEBAQCAuLg4rFq1ChMmTAAAjBo1CuPGjcNbb72FlJQUdOjQofqZfFlZWXjxxRehUv3v90iVSoW8vLzq7xs1alT9Z6vVig8++ADr1q3DtWvXqtfLz89HWVkZLBYLGjduXP3+n/85MzMThw8frp4+rNregw8+WKefsy7rBwYGVv/ZYDAgKCioxvclJSU1tvnzfKGhocjNzQVQ+bkkJCTUeDpMRUVF9fJfrgtU/n+YN28eMjMzAQAlJSXIz8+v0892K/b8/Kh+YylSvVBWVoa1a9fCZrMhOjoaAFBeXo4bN27gxIkTaNeuHcLDwxEaGoqtW7dizZo1iIuLq16/UaNGePvtt9GjR49fbfvSpUsAAEmSql9bvXo1Nm3ahHnz5qFp06YoLCxEVFQUZFlGQEAANBoNcnJyEBYWBgDIzs6uXrdx48aIiorCvHnz7upnvdf1b+bn+bKyshASElI91qRJk/DCCy/cct2ffy6ZmZn4v//7P8yfPx+RkZFQq9V46KGHbvreKkajEaWlpdXfX716tdYxHPHzU/3B6VOqFzZu3Ai1Wo2kpCQkJCQgISEBycnJ6NmzZ40TbuLi4vDtt99i3759iImJqX79iSeewIcffli9d3Pt2jVs3LjxluMVFxdDp9PB398fpaWlmDVrVvUytVqNYcOG4dNPP0VpaSkyMjKQmJhYvXzQoEE4d+4cEhISUFFRgYqKChw+fBgZGRk3HSsoKAgXL1686/XrYtGiRcjJyUFBQQE+//xzjBw5EgDw6KOPYsmSJfjxxx8hyzJKSkqwZcsWFBUV3XQ7paWlkCSpem995cqVNU5ACgwMxOXLl2tcLtO+fXukpKSgtLQU58+fx4oVK2rN6oifn+oPliLVC6tWrcLDDz+M0NBQBAcHV3899dRTWL16dfWxwbi4OOzbtw99+vSp/ocbAH7zm99gyJAhmDhxIiIjI/HYY4/Vehxs9OjRCA0NxX333YfY2Fh069atxvJp06ahsLAQ0dHReP311xEbGwudTgcA8Pb2xtdff43k5GTcd9996N+/P/7973/f8rrK3/zmN1i/fj2ioqIwc+bMO16/LuLi4jBx4kQMHToUzZs3r94z7Ny5M/7xj39gxowZiIqKwvDhwxEfH3/L7YSHh2PixIkYN24c+vXrh1OnTtV4yHSfPn0QHh6O/v37o3fv3gCAZ555BlqtFv369cMbb7xRfUbwrTji56f6gw8ZJnIB77//Pq5evYp//etfoqP8ypAhQzBz5kz069dPdBQih+OeIpEAGRkZOHHiBGRZxuHDh7FixQoMGzZMdCyieo8n2hAJUFxcjNdeew25ubkIDAzExIkTcf/994uORVTvcfqUiIhIwelTIiIiBUuRiIhIwVIkIiJSsBSJiIgULEUiIiIFS5GIiEjx//GISSezqI9TAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 504x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "samples = fit.extract(permuted=True)\n",
    "print(\"std(mu0): {:.2f}\".format(np.std(samples['mu0'])))\n",
    "mu = samples['mu']\n",
    "\n",
    "# matrix of probabilities that one mu is larger than other\n",
    "ps = np.zeros((3, 3))\n",
    "for k1 in range(3):\n",
    "    for k2 in range(k1+1, 3):\n",
    "        ps[k1, k2] = np.mean(mu[:, k1] > mu[:, k2])\n",
    "        ps[k2, k1] = 1 - ps[k1, k2]\n",
    "print(\"Matrix of probabilities that one mu is larger than other:\")\n",
    "print(ps)\n",
    "\n",
    "months = ['June', 'July', 'August']\n",
    "fig, ax = az.plot_forest(fit,\n",
    "                           kind='ridgeplot',\n",
    "                           var_names=['mu'],\n",
    "                           combined=True,\n",
    "                           ridgeplot_overlap=1,\n",
    "                           r_hat=False,\n",
    "                           n_eff=False,\n",
    "                           figsize=(7, 7))\n",
    "ax[0].set_yticklabels(months[::-1])\n",
    "ax[0].set_xlabel('Average temperature');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
